0
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

2. 1500 families with 2 children were selected randomly, and the following data were recorded:
Number of girls in a family210
Number of families           475                   814                 211       
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.

Answer

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.

3. Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August. 
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:
Outcome            3 heads          2 heads        1 head        No head     
Frequency23727728
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:
Monthly income
(in ₹)
Vehicles per family
012Above 2
Less than 700010160250
7000-100000305272
10000-130001535291
13000-1600024695925
16000 or more15798288
Suppose a family is chosen. Find the probability that the family chosen is
(i) earning ₹10000 – 13000 per month and owning exactly 2 vehicles.
(ii) earning ₹16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than ₹7000 per month and does not own any vehicle.
(iv) earning ₹13000 – 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle. 

Answer

Total numbers of families = 2400

(i) Numbers of families earning ₹10000 –13000 per month and owning exactly 2 vehicles = 29
Required probability = 29/2400

(ii) Number of families earning ₹16000 or more per month and owning exactly 1 vehicle = 579
Required probability = 579/2400

(iii) Number of families earning less than ₹7000 per month and does not own any vehicle = 10 Required probability = 10/2400 = 1/240

(iv) Number of families earning ₹13000-16000 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.

MarksNumber of students
0 - 207
20 - 3010
30 - 4010
40 - 5020
50 - 6020
60 - 7015
70 - above8
Total90

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.
OpinionNumber of students
like135
dislike65
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?

Answer

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.

Answer

Total numbers of bags = 11
Numbers of bags containing more than 5 kg of flour = 7
Required probability = 7/11

12. 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


For any Problem and Query Please
Email us at ravichaubey43@gmail.com
Or call us on mobile 9529011055...

Please comment below the post to
Make NationRead Best at Google.

*NationRead since 2014*

Post a Comment

 
Top