Access Answers for SAT Maths Chapter 15 – Probability
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.
Solution:
According to the question,
Total number of balls = 30
Numbers of boundary = 6
Number of time batswoman 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 family 2 1 0
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.
Solution:
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 girl = 814
Probability = Numbers of families having 1 girl/Total numbers of families
= 814/1500 = 407/750
(iii) Numbers of families having 0 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.
Solution:
Total numbers of students in the class = 40
Numbers of students born in August = 6
The probability that a student of the class was born in August, = 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
Frequency 23 72 77 28
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Solution:
Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200
∴, the probability of 2 heads coming up = 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:
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.
Solution:
According to the question,
Total number of balls = 30
Numbers of boundary = 6
Number of time batswoman 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 family 2 1 0
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.
Solution:
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 girl = 814
Probability = Numbers of families having 1 girl/Total numbers of families
= 814/1500 = 407/750
(iii) Numbers of families having 0 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.
Solution:
Total numbers of students in the class = 40
Numbers of students born in August = 6
The probability that a student of the class was born in August, = 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
Frequency 23 72 77 28
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Solution:
Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200
∴, the probability of 2 heads coming up = 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:
