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**Exercise 15.1****1. In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. Answer**

Total numbers of balls = 30

Numbers of boundary = 6

Numbers of time she didn't hit boundary = 30 - 6 = 24

Probability she did not hit a boundary = 24/30 = 4/5

**Compute the probability of a family, chosen at random, having (i) 2 girls **

**(ii) 1 girl **

**(iii) No girl Also check whether the sum of these probabilities is 1.**

Total numbers of families = 1500

(i) Numbers of families having 2 girls = 475

Probability = Numbers of families having 2 girls/Total numbers of families

= 475/1500 = 19/60

(ii) Numbers of families having 1 girls = 814

Probability = Numbers of families having 1 girls/Total numbers of families

= 814/1500 = 407/750

(iii) Numbers of families having 2 girls = 211

Probability = Numbers of families having 0 girls/Total numbers of families

= 211/1500

Sum of the probability = 19/60 + 407/750 + 211/1500

= (475 + 814 + 211)/1500 = 1500/1500 = 1

Yes, the sum of these probabilities is 1.

Answer

Total numbers of students = 40

Numbers of students = 6

Required probability = 6/40 = 3/20**4. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:**

**If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.****Answer**

Number of times 2 heads come up = 72

Total number of times the coins were tossed = 200

Required probability = 72/200 = 9/25**5. An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:**

**Suppose a family is chosen. Find the probability that the family chosen is**

**(i) earning â‚¹10000 â€“ 13000 per month and owning exactly 2 vehicles. (ii) earning â‚¹16000 or more per month and owning exactly 1 vehicle. (iii) earning less than â‚¹7000 per month and does not own any vehicle. (iv) earning â‚¹13000 â€“ 16000 per month and owning more than 2 vehicles. (v) owning not more than 1 vehicle. **

Total numbers of families = 2400

(i) Numbers of families earning â‚¹10000 â€“13000 per month and owning exactly 2 vehicles = 29

Required probability = 29/2400

(ii) Number of families earning â‚¹16000 or more per month and owning exactly 1 vehicle = 579

Required probability = 579/2400

(iii) Number of families earning less than â‚¹7000 per month and does not own any vehicle = 10 Required probability = 10/2400 = 1/240

(iv) Number of families earning â‚¹13000-16000 per month and owning more than 2 vehicles = 25

Required probability = 25/2400 = 1/96

(v) Number of families owning not more than 1 vehicle = 10+160+0+305+1+535+2+469+1+579 = 2062

Required probability = 2062/2400 = 1031/1200

**6. Refer to Table 14.7, Chapter 14. (i) Find the probability that a student obtained less than 20% in the mathematics test. (ii) Find the probability that a student obtained marks 60 or above.**

**Answer**

Total numbers of students = 90

(i) Numbers of students obtained less than 20% in the mathematics test = 7

Required probability = 7/90

(ii) Numbers of student obtained marks 60 or above = 15+8 = 23

Required probability = 23/90**7. To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.**

**Find the probability that a student chosen at random (i) likes statistics, **

**(ii) does not like it.**

**Answer**

Total numbers of students = 135 + 65 = 200

(i) Numbers of students who like statistics = 135

Required probability = 135/200 = 27/40

(ii) Numbers of students who does not like statistics = 65

Required probability = 65/200 = 13/40**8. Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives: (i) less than 7 km from her place of work? (ii) more than or equal to 7 km from her place of work? (iii) within 1/2 km from her place of work?**

The distance (in km) of 40 engineers from their residence to their place of work were found as follows:

5 , 3 , 10 , 20 , 25 , 11 , 13 , 7 , 12 , 31 , 19 , 10 , 12 , 17 , 18 , 11 , 3 , 2 , 17 , 16 , 2 , 7 , 9 , 7 , 8 , 3 , 5 , 12 , 15 , 18 , 3 , 12 , 14 , 2 , 9 , 6 , 15 , 15 , 7 , 6 , 12

Total numbers of engineers = 40

(i) Numbers of engineers living less than 7 km from her place of work = 9

Required probability = 9/40

(ii) Numbers of engineers living less than 7 km from her place of work = 40 - 9 = 31

Required probability = 31/40

(iii) Numbers of engineers living less than 7 km from her place of work = 0

Required probability = 0/40 = 0**11. Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg): 4.97 , 5.05 , 5.08 5.03 5.00 5.06 5.08 , 4.98 , 5.04 , 5.07 , 5.00 Find the probability that any of these bags chosen at random contains more than 5 kg of flour.**

Total numbers of bags = 11

Numbers of bags containing more than 5 kg of flour = 7

Required probability = 7/11

**In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12-0.16 on any of these days. The data obtained for 30 days is as follows: 0.03 , 0.08 , 0.08 , 0.09 , 0.04 , 0.17 , 0.16 , 0.05 , 0.02 , 0.06 , 0.18 , 0.20 , 0.11 , 0.08 , 0.12 , 0.13 , 0.22 , 0.07 , 0.08 , 0.01 , 0.10 , 0.06 , 0.09 , 0.18 , 0.11 , 0.07 , 0.05 , 0.07 , 0.01 , 0.04**

**Answer**

Total numbers of days data recorded = 30 days

Numbers of days in which sulphur dioxide in the interval 0.12-0.16 = 2

Required probability = 2/30 = 1/15**13. In Q.1, Exercise 14.2, you were asked to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB. The blood groups of 30 students of Class VIII are recorded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.**

**Answer**

Total numbers of students = 30

Numbers of students having blood group AB = 3

Required probability = 3/30 = 1/10

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