Chapter 13 – Statistics And Probability

Class 10 Mathematics · 79 questions · 74 with answers

Solved examples

Ex. 1Multiple choice

Construction of a cumulative frequency table is useful in determining the

(A)mean
(B)median
(C)mode
(D)all the above three measures

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Solution : Answer (B)

Ex. 2Multiple choice

In the following distribution : Monthly income range (in Rs) Number of families Income more than Rs 10000 100 Income more than Rs 13000 85 Income more than Rs 16000 69 Income more than Rs 19000 50 Income more than Rs 22000 33 Income more than Rs 25000 15 the number of families having income range (in Rs) 16000 – 19000 is

(A)15
(B)16
(C)17
(D)19

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Solution : Answer (D)

Ex. 3Multiple choice

Consider the following frequency distribution of the heights of 60 students of a class : Height (in cm) Number of students 150-155 15 155-160 13 160-165 10 165-170 8 170-175 9 175-180 5 The sum of the lower limit of the modal class and upper limit of the median class is

(A)310
(B)315
(C)320
(D)330

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Solution : Answer (B)

Ex. 4Multiple choice

Which of the the following can be the probability of an event? 18 8

(A)– 0.04
(B)1.004
(C)
(D)23 7

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Solution : Answer (C) STATISTICS AND PROBABILITY 157

Ex. 5Short answer

A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is

Ex. 6Multiple choice

A bag contains 3 red balls, 5 white balls and 7 black balls. What is the probability that a ball drawn from the bag at random will be neither red nor black? 1 1 7 8

Ex. 1Short answerExercise 13.1

The mean of ungrouped data and the mean calculated when the same data is grouped are always the same. Do you agree with this statement? Give reason for your answer.

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Solution : The statement is not true. The reason is that when we calculated mean of a grouped data, it is assumed that frequency of each class is centred at the mid-point of the class. Because of this, two values of the mean, namely, those from ungrouped and grouped data are rarely the same.

Ex. 2Short answerExercise 13.1

Is it correct to say that an ogive is a graphical representation of a frequency distribution? Give reason.

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Solution : Graphical representation of a frequency distribution may not be an ogive. It may be a histogram. An ogive is a graphical representation of cumulative frequency distribution.

Ex. 3True / FalseExercise 13.1

In any situation that has only two possible outcomes, each outcome will have probability . True or false? Why?

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Solution : False, because the probability of each outcome will be only when the two outcomes are equally likely otherwise not.

Ex. 1Short answerExercise 13.2

Construct the cumulative frequency distribution of the following distribution : Class 12.5-17.5 17.5-22.5 22.5-27.5 27.5-32.5 32.5-37.5 Frequency 2 22 19 14 13

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Solution : The required cumulative frequency distribution of the given distribution is given below : Class Frequency Cumulative frequency 12.5-17.5 2 2 17.5-22.5 22 24 22.5-27.5 19 43 27.5-32.5 14 57 32.5-37.5 13 70

Ex. 2Short answerExercise 13.2

Daily wages of 110 workers, obtained in a survey, are tabulated below : Daily wages (in Rs) Number of workers 100-120 10 120-140 15 140-160 20 160-180 22 180-200 18 200-220 12 220-240 13 Compute the mean daily wages of these workers.

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Solution : We first find the classmark, xi, of each class and then proceed as follows: Daily wages Class marks Number of workers f ix i (in Rs) (x i) (f i) Classes 100-120 110 10 1100 120-140 130 15 1950 140-160 150 20 3000 160-180 170 22 3740 180-200 190 18 3420 200-220 210 12 2520 220-240 230 13 2990 fi = 110, fi xi = 18720 fi xi 18720 Therefore, Mean = x = = = 170.20 fi 110 Hence, the mean daily wages of the workers is Rs 170.20. Note : Mean daily wages can also be calculated by the assumed mean method or step deviation method.

Ex. 3Short answerExercise 13.2

The percentage of marks obtained by 100 students in an examination are given below: Marks 30-35 35-40 40-45 45-50 50-55 55-60 60-65 Frequency 14 16 18 23 18 8 3 Determine the median percentage of marks.

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Solution : Marks Number of Students Cumulative frequency (Class) (Frequency) 30-35 14 14 35-40 16 30 40-45 18 48 45-50 23 71 ← Median class 50-55 18 89 55-60 8 97 60-65 3 100 STATISTICS AND PROBABILITY 165 Here, n = 100. Therefore, = 50, This observation lies in the class 45-50. l (the lower limit of the median class) = 45 cf (the cumulative frequency of the class preceding the median class) = 48 f (the frequency of the median class) = 23 h (the class size) = 5 n 2 − cf Median = l + h f 50 − 48 = 45 + ×5 23 = 45 + = 45.4 So, the median percentage of marks is 45.4.

Ex. 4Short answerExercise 13.2

The frequency distribution table of agricultural holdings in a village is given below : Area of land (in hectares) 1-3 3-5 5-7 7-9 9-11 11-13 Number of families 20 45 80 55 40 12 Find the modal agricultural holdings of the village.

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Solution : Here the maximum class frequency is 80, and the class corresponding to this frequency is 5-7. So, the modal class is 5-7. l ( lower limit of modal class) = 5 f1 (frequency of the modal class) = 80 f0 (frequency of the class preceding the modal class) = 45 f2 (frequency of the class succeeding the modal class) = 55 h (class size) = 2 f1 − f0 Mode = l + ×h 2 f1 − f0 − f 2 80 – 45 =5 + ×2 2(80) − 45 − 55

Ex. 1Short answerExercise 13.3

The following is the cumulative frequency distribution (of less than type) of 1000 persons each of age 20 years and above. Determine the mean age. Age below (in years) 30 40 50 60 70 80 Number of persons 100 220 350 750 950 1000

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Solution : First, we make the frequency distribution of the given data and then proceed to calculate mean by computing class marks (xi), ui’s and fiui’s as follows : x – 45 Class Frequency Class mark ui = i fi u i (fi ) (x i ) 20-30 100 25 –2 –200 30-40 120 35 –1 –120 40-50 130 45 0 0 50-60 400 55 1 400 60-70 200 65 2 400 70-80 50 75 3 150 fi = 1000 fi ui = 630

Questions

Q3Multiple choice

4 6 9

(A)
(B)
(C)
(D)13 13 13 13 Solution : Answer (A)

Q5Multiple choice

3 15 15 Solution : Answer (B)

Q1Multiple choiceExercise 13.1

In the formula x = a+ fi , for finding the mean of grouped data di’s are deviations from a of

(A)lower limits of the classes
(B)upper limits of the classes
(C)mid points of the classes
(D)frequencies of the class marks

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Q2Multiple choiceExercise 13.1

While computing mean of grouped data, we assume that the frequencies are

(A)evenly distributed over all the classes
(B)centred at the classmarks of the classes
(C)centred at the upper limits of the classes
(D)centred at the lower limits of the classes

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(B) centred at the classmarks of the classes

Q3Multiple choiceExercise 13.1

If xi’s are the mid points of the class intervals of grouped data, fi’s are the corresponding frequencies and x is the mean, then ( fi xi − x ) is equal to

(A)0
(B)–1
(C)1
(D)2

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(A) 0

Q4Multiple choiceExercise 13.1

In the formula x = a + h , for finding the mean of grouped frequency distribution, ui = xi + a xi – a a – xi

(A)
(B)h (xi – a)
(C)
(D)h h h

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(C)

Q5Multiple choiceExercise 13.1

The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its

(A)mean
(B)median
(C)mode
(D)all the three above

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(B) median

Q6Multiple choiceExercise 13.1

For the following distribution : Class 0-5 5-10 10-15 15-20 20-25 Frequency 10 15 12 20 9 the sum of lower limits of the median class and modal class is

(A)15
(B)25
(C)30
(D)35

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(B) 25

Q7Multiple choiceExercise 13.1

Consider the following frequency distribution : Class 0-5 6-11 12-17 18-23 24-29 Frequency 13 10 15 8 11 The upper limit of the median class is

(A)17
(B)17.5
(C)18
(D)18.5

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(B) 17.5

Q8Multiple choiceExercise 13.1

For the following distribution : Marks Number of students Below 10 3 Below 20 12 Below 30 27 Below 40 57 Below 50 75 Below 60 80 the modal class is

(A)10-20
(B)20-30
(C)30-40
(D)50-60

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Q9Multiple choiceExercise 13.1

Consider the data : Class 65-85 85-105 105-125 125-145 145-165 165-185 185-205 Frequency 4 5 13 20 14 7 4 STATISTICS AND PROBABILITY 159 The difference of the upper limit of the median class and the lower limit of the modal class is

(A)0
(B)19
(C)20
(D)38

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Q10Multiple choiceExercise 13.1

The times, in seconds, taken by 150 atheletes to run a 110 m hurdle race are tabulated below : Class 13.8-14 14-14.2 14.2-14.4 14.4-14.6 14.6-14.8 14.8-15 Frequency 2 4 5 71 48 20 The number of atheletes who completed the race in less then 14.6 seconds is :

(A)11
(B)71
(C)82
(D)130

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Q11Multiple choiceExercise 13.1

Consider the following distribution : Marks obtained Number of students More than or equal to 0 63 More than or equal to 10 58 More than or equal to 20 55 More than or equal to 30 51 More than or equal to 40 48 More than or equal to 50 42 the frequency of the class 30-40 is

(A)3
(B)4
(C)48
(D)51

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(A) 3

Q12Multiple choiceExercise 13.1

If an event cannot occur, then its probability is 3 1

(A)1
(B)
(C)
(D)0 4 2

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(D) 0 4 2

Q13Short answerExercise 13.1

Which of the following cannot be the probability of an event?

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(D)

Q1Multiple choiceExercise 13.1

(A)
(B)0.1
(C)3%
(D)

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Q3Multiple choiceExercise 13.1

16 14. An event is very unlikely to happen. Its probability is closest to

(A)0.0001
(B)0.001
(C)0.01
(D)0.1 15. If the probability of an event is p, the probability of its complementary event will be (A) p–1 (B) p (C) 1–p (D) 1 − 16. The probability expressed as a percentage of a particular occurrence can never be (A) less than 100 (B) less than 0 (C) greater than 1 (D) anything but a whole number 17. If P(A) denotes the probability of an event A, then (A) P(A) < 0 (B) P(A) > 1 (C) 0 ≤ P(A) ≤ 1 (D) –1 ≤ P(A) ≤ 1 18. A card is selected from a deck of 52 cards. The probability of its being a red face card is 3 3 2 1 (A) (B) (C) (D) 26 13 13 2 19. The probability that a non leap year selected at random will contain 53 sundays is

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(A) 0.0001

Q1Multiple choiceExercise 13.1

2 3 5

(A)
(B)
(C)
(D)7 7 7 7 20. When a die is thrown, the probability of getting an odd number less than 3 is

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(C)

Q1Multiple choiceExercise 13.1

1 1

(A)
(B)
(C)
(D)0 6 3 2 21. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is (A) 4 (B) 13 (C) 48 (D) 51 22. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is (A) 7 (B) 14 (C) 21 (D) 28 23. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought? (A) 40 (B) 240 (C) 480 (D) 750 24. One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is

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(C)

Q1Multiple choiceExercise 13.1

3 4 1

(A)
(B)
(C)
(D)5 5 5 3 25. Someone is asked to take a number from 1 to 100. The probability that it is a prime is

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(C)

Q1Multiple choiceExercise 13.1

6 1 13

(A)
(B)
(C)
(D)5 25 4 50 STATISTICS AND PROBABILITY 161 26. A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is

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(C)

Q4Multiple choiceExercise 13.1

6 8 17

(A)
(B)
(C)
(D)23 23 23 23

Show answer

(C)

Q1Short answerExercise 13.2

The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement? Give reason.

Show answer

Not always, because for calculating median of a grouped data, the formula used is based on the assumption that the observations in the classes are uniformly distributed (or equally spaced).

Q2Short answerExercise 13.2

In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula x = a+ fi where a is the assumed mean. a must be one of the mid-points of the classes. Is the last statement correct? Justify your answer.

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Not necessary, the mean of the data does not depend on the choice of a (assumed tt © mean).

Q3Short answerExercise 13.2

Is it true to say that the mean, mode and median of grouped data will always be different? Justify your answer.

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No, it is not always the case. The values of these three measures can be the same. It depends on the type of data.

Q4Short answerExercise 13.2

Will the median class and modal class of grouped data always be different? Justify your answer.

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Not always. It depends on the data.

Q5Short answerExercise 13.2

In a family having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is . Is this correct? Justify your answer.

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No, the outcomes are not equally likely. For example, outcome ‘one girl’ means gbb, bgb, bbg ‘three girls’ means ggg and so on.

Q6Short answerExercise 13.2

A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3) (Fig. 13.1). Are the outcomes 1, 2 and 3 equally likely to occur? Give reasons.

This question refers to a figure in the original PDF.

Show answer

No, the outcomes are not equally likely. The outcome ‘3’ is more likely than the others.

Q7Short answerExercise 13.2

Apoorv throws two dice once and computes the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36? Why?

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Peehu; probability of Apoorv’s getting 36 while probability of Peehu’s getting 1 6 36 . 6 36

Q8Short answerExercise 13.2

When we toss a coin, there are two possible outcomes - Head or Tail. Therefore, the probability of each outcome is . Justify your answer.

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Yes, the probability of each outcome is , since the two outcomes are equally likely. 1 5

Q9Short answerExercise 13.2

A student says that if you throw a die, it will show up 1 or not 1. Therefore, the probability of getting 1 and the probability of getting ‘not 1’ each is equal to . Is this correct? Give reasons.

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No, outcomes ‘1’ and ‘not 1’ are not equally likely, P (1) = , P (not 1) = , 6 6

Q10Short answerExercise 13.2

I toss three coins together. The possible outcomes are no heads, 1 head, 2 heads and 3 heads. So, I say that probability of no heads is . What is wrong with this conclusion?

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No, the outcomes are not equally likely. Outcome ‘no head’ means ‘TTT’; outcome 1 3 ‘one head’ means THT, HTT, TTH and so on. P (TTT) = , P (one head) = and 8 8 so on.

Q11Short answerExercise 13.2

If you toss a coin 6 times and it comes down heads on each occasion. Can you say that the probability of getting a head is 1? Give reasons. STATISTICS AND PROBABILITY 163

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No, the outcomes ‘head’ and ‘tail’ are equally likely every time regardless of what you get in a few tosses.

Q12Short answerExercise 13.2

Sushma tosses a coin 3 times and gets tail each time. Do you think that the outcome of next toss will be a tail? Give reasons.

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It could be a tail or head as both the outcomes are equally likely, in each toss.

Q13Short answerExercise 13.2

If I toss a coin 3 times and get head each time, should I expect a tail to have a higher chance in the 4th toss? Give reason in support of your answer.

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No, head and tail are equally likely. So, no question of expecting a tail to have a higher chance in the 4th toss.

Q14Short answerExercise 13.2

A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since this situation has only two possible outcomes, so, the probability of each is . Justify.

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Yes, the outcomes ‘odd number’, ‘even number’ are equally likely in the situation considered.

Q35Short answerExercise 13.2

35 =5+ × 2 =5+ 60 30 = 5 + 1.2 = 6.2 Hence, the modal agricultural holdings of the village is 6.2 hectares.

Q1Short answerExercise 13.3

Find the mean of the distribution : Class 1-3 3-5 5-7 7-10 Frequency 9 22 27 17

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5.5

Q2Short answerExercise 13.3

Calculate the mean of the scores of 20 students in a mathematics test : Marks 10-20 20-30 30-40 40-50 50-60 Number of students 2 4 7 6 1

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Q3Short answerExercise 13.3

Calculate the mean of the following data : Class 4–7 8 –11 12– 15 16 –19 Frequency 5 4 9 10 STATISTICS AND PROBABILITY 167

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12.93

Q4Short answerExercise 13.3

The following table gives the number of pages written by Sarika for completing her own book for 30 days : Number of pages written per day 16-18 19-21 22-24 25-27 28-30 Number of days 1 3 4 9 13 Find the mean number of pages written per day.

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Q5Short answerExercise 13.3

The daily income of a sample of 50 employees are tabulated as follows : Income (in Rs) 1-200 201-400 401-600 601-800 Number of employees 14 15 14 7 Find the mean daily income of employees.

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Rs. 356.5

Q6Short answerExercise 13.3

An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table : Number of seats 100-104 104-108 108-112 112-116 116-120 Frequency 15 20 32 18 15 Determine the mean number of seats occupied over the flights.

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109. 92

Q7Short answerExercise 13.3

The weights (in kg) of 50 wrestlers are recorded in the following table : Weight (in kg) 100-110 110-120 120-130 130-140 140-150 Number of wrestlers 4 14 21 8 3 Find the mean weight of the wrestlers.

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123.4 kg

Q8Short answerExercise 13.3

The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below : Mileage (km/l) 10-12 12-14 14-16 16-18 Number of cars 7 12 18 13 Find the mean mileage. The manufacturer claimed that the mileage of the model was 16 km/litre. Do you agree with this claim?

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14.48 km/l; No, the manufacturer is claiming tt © mileage 1.52 km/h more than the average mileage

Q9Short answerExercise 13.3

The following is the distribution of weights (in kg) of 40 persons : Weight (in kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 Number of persons 4 4 13 5 6 5 2 1 Construct a cumulative frequency distribution (of the less than type) table for the data above.

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Weight (in kg) Number of persons Less then 45 4 Less then 50 8 Less then 55 21 Less then 60 26 Less then 65 32 Less then 70 37 Less then 75 39 Less then 80 40 ANSWERS 199

Q10Short answerExercise 13.3

The following table shows the cumulative frequency distribution of marks of 800 students in an examination: Marks Number of students Below 10 10 Below 20 50 Below 30 130 Below 40 270 Below 50 440 Below 60 570 Below 70 670 Below 80 740 Below 90 780 Below 100 800 Construct a frequency distribution table for the data above. STATISTICS AND PROBABILITY 169

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Marks Number of students 0-10 10 10-20 40 20-30 80 30-40 140 40-50 170 50-60 130 pu T 60-70 100 70-80 70 80-90 40

Q11Short answerExercise 13.3

Form the frequency distribution table from the following data : Marks (out of 90) Number of candidates More than or equal to 80 4 More than or equal to 70 6 More than or equal to 60 11 More than or equal to 50 17 More than or equal to 40 23 More than or equal to 30 27 More than or equal to 20 30 More than or equal to 10 32 More than or equal to 0 34

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bl 90-100 Marks Number of candidates 0-10 2 10-20 2 20-30 3 30-40 4 tt © 40-50 6 50-60 6 60-70 5 70-80 2 80-90 4

Q12Short answerExercise 13.3

Find the unknown entries a, b, c, d, e, f in the following distribution of heights of students in a class : Height Frequency Cumulative frequency (in cm) 150-155 12 a 155-160 b 25 160-165 10 c 165-170 d 43 170-175 e 48 175-180 2 f Total 50

Show answer

a = 12, b = 13, c = 35, d = 8, e = 5, f = 50

Q13Multiple choiceExercise 13.3

The following are the ages of 300 patients getting medical treatment in a hospital on a particular day : Age (in years) 10-20 20-30 30-40 40-50 50-60 60-70 Number of patients 60 42 55 70 53 20 Form:

(i)Less than type cumulative frequency distribution.
(ii)More than type cumulative frequency distribution.

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(i) Less than type cumulative frequency distribution.

(ii) More than type cumulative frequency distribution.

Q14Short answerExercise 13.3

Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class : Marks Below 20 Below 40 Below 60 Below 80 Below 100 Number of students 17 22 29 37 50 Form the frequency distribution table for the data.

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bl Marks NKPN Number of students 20-40 5 40-60 7 60-80 8 80-100 13 tt ©

Q15Short answerExercise 13.3

Weekly income of 600 families is tabulated below : Weekly income Number of families (in Rs) 0-1000 250 1000-2000 190 2000-3000 100 3000-4000 40 4000-5000 15 5000-6000 5 Total 600 Compute the median income.

Show answer

Rs 1263.15

Q16Short answerExercise 13.3

The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows : Speed (km/h) 85-100 100-115 115-130 130-145 Number of players 11 9 8 5 Calculate the median bowling speed. STATISTICS AND PROBABILITY 171

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109.17 km/h

Q17Short answerExercise 13.3

The monthly income of 100 families are given as below : Income (in Rs) Number of families 0-5000 8 5000-10000 26 10000-15000 41 15000-20000 16 20000-25000 3 25000-30000 3 30000-35000 2 35000-40000 1 Calculate the modal income.

Show answer

Rs 11875 1 5 1 5

Q18Short answerExercise 13.3

The weight of coffee in 70 packets are shown in the following table : Weight (in g) Number of packets 200-201 12 201-202 26 202-203 20 203-204 9 204-205 2 205-206 1 Determine the modal weight.

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201.7 kg

Q19Multiple choiceExercise 13.3

Two dice are thrown at the same time. Find the probability of getting

(i)same number on both dice.
(ii)different numbers on both dice.

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(i) same number on both dice.

(ii) different numbers on both dice.

Q20Multiple choiceExercise 13.3

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is

(i)7?
(ii)a prime number?
(iii)1?

Show answer

(i) 7?

(ii) a prime number?

(iii) 1?

Q21Multiple choiceExercise 13.3

Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is

(i)6
(ii)12
(iii)7

Show answer

(i) 6

(ii) 12

(iii) 7

Q22Short answerExercise 13.3

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is less than 9.

Show answer

9 9 9 1 1 1 1 1 1 1 1

Q23Short answerExercise 13.3

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3, respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.

Show answer

P (2) = , P (3) = , P (4) = , P (5) = , P (6) = , P (7) = , P (8)= P (9) = 18 9 6 6 6 6 9 18 3 1 1 2

Q24Short answerExercise 13.3

A coin is tossed two times. Find the probability of getting at most one head.

Q25Multiple choiceExercise 13.3

A coin is tossed 3 times. List the possible outcomes. Find the probability of getting

(i)all heads
(ii)at least 2 heads

Show answer

(i) all heads

(ii) at least 2 heads

Q26Short answerExercise 13.3

Two dice are thrown at the same time. Determine the probabiity that the difference of the numbers on the two dice is 2.

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4 8 2 9 5 7 17

Q27Multiple choiceExercise 13.3

A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random. Find the probability of this ball being a

(i)red ball
(ii)green ball
(iii)not a blue ball

Show answer

(i) red ball

(ii) green ball

(iii) not a blue ball

Q28Multiple choiceExercise 13.3

The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is

(i)a heart
(ii)a king

Show answer

(i) a heart

(ii) a king

Q29Multiple choiceExercise 13.3

Refer to Q.28. What is the probability that the card is

(i)a club
(ii)10 of hearts

Show answer

(i) a club

(ii) 10 of hearts

Q30Multiple choiceExercise 13.3

All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value

(i)7
(ii)greater than 7
(iii)less than 7

Show answer

(i) 7

(ii) greater than 7

(iii) less than 7

Q31Multiple choiceExercise 13.3

An integer is chosen between 0 and 100. What is the probability that it is

(i)divisible by 7?
(ii)not divisible by 7?

Show answer

(i) divisible by 7?

(ii) not divisible by 7?

Q32Multiple choiceExercise 13.3

Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has

(i)an even number
(ii)a square number STATISTICS AND PROBABILITY 173

Show answer

(i) an even number

(ii) a square number STATISTICS AND PROBABILITY 173

Q33Short answerExercise 13.3

A letter of English alphabets is chosen at random. Determine the probability that the letter is a consonant.

Q34Short answerExercise 13.3

There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of Rs 100 each, 100 of them contain a cash prize of Rs 50 each and 200 of them contain a cash prize of Rs 10 each and rest do not contain any cash prize. If they are well shuffled and an envelope is picked up out, what is the probability that it contains no cash prize?

Show answer

0.69

Q35Short answerExercise 13.3

Box A contains 25 slips of which 19 are marked Re 1 and other are marked Rs 5 each. Box B contains 50 slips of which 45 are marked Re 1 each and others are marked Rs 13 each. Slips of both boxes are poured into a third box and resuffled. A slip is drawn at random. What is the probability that it is marked other than Re 1?

Show answer

26 75 3 5

Q36Short answerExercise 13.3

A carton of 24 bulbs contain 6 defective bulbs. One bulbs is drawn at random. What is the probability that the bulb is not defective? If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective?

Show answer

P (not defective) = , P (2nd bulb defective) = 4 23

Q37Multiple choiceExercise 13.3

A child’s game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a

(i)triangle
(ii)square
(iii)square of blue colour
(iv)triangle of red colour

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(i) triangle

(ii) square

(iii) square of blue colour

(iv) triangle of red colour

Q38Multiple choiceExercise 13.3

In a game, the entry fee is Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she

(i)loses the entry fee.
(ii)gets double entry fee.
(iii)just gets her entry fee.

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(i) loses the entry fee.

(ii) gets double entry fee.

(iii) just gets her entry fee.

Q39Multiple choiceExercise 13.3

A die has its six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total score is recorded.

(i)How many different scores are possible?
(ii)What is the probability of getting a total of 7?

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(i) How many different scores are possible?

(ii) What is the probability of getting a total of 7?

Q40Multiple choiceExercise 13.3

A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defects and 3 have major defects. Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is

(i)acceptable to Varnika?
(ii)acceptable to the trader?

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(i) acceptable to Varnika?

(ii) acceptable to the trader?

Q41Multiple choiceExercise 13.3

A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is

(i)not red?
(ii)white?

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(i) not red?

(ii) white?

Q42Multiple choiceExercise 13.3

At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that

(i)the first player wins a prize?
(ii)the second player wins a prize, if the first has won?

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(i) the first player wins a prize?

(ii) the second player wins a prize, if the first has won?

Hint: Hint : (ii) After first player has won the prize the number of perfect squares greater than 500 will be reduced by 1