Q1. 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:
Total number of balls played = 30
Number of times boundary was hit = 6
Number of times boundary was not hit = \(30-6=24\)

\(
\text{Probability}
=\frac{\text{Number of times boundary was not hit}}{\text{Total number of balls}}
=\frac{24}{30}
=\frac{4}{5}
\)

Q2. 1500 families with 2 children were selected randomly, and the following data were recorded.

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 number of families = 1500

(i)

\(
\text{Probability}
=\frac{475}{1500}
=\frac{19}{60}
\)

(ii)

\(
\text{Probability}
=\frac{814}{1500}
=\frac{407}{750}
\)

(iii)

\(
\text{Probability}
=\frac{211}{1500}
\)

\(
\text{Sum of probabilities}
=\frac{475+814+211}{1500}
=\frac{1500}{1500}
=1
\)

Q3. Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August.

Solution:
Total number of students = 40
Number of students born in August = 6

\(
\text{Probability}
=\frac{6}{40}
=\frac{3}{20}
\)

Q4. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes.

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

Solution:
Number of times 2 heads occurred = 72
Total number of trials = 200

\(
\text{Probability}
=\frac{72}{200}
=\frac{9}{25}
\)

Q5. 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.

Solution:
Total number of families = 2400

(i) \(\text{Probability}=\frac{29}{2400}\)

(ii) \(\text{Probability}=\frac{579}{2400}\)

(iii) \(\text{Probability}=\frac{10}{2400}=\frac{1}{240}\)

(iv) \(\text{Probability}=\frac{25}{2400}=\frac{1}{96}\)

(v) Number of families owning not more than 1 vehicle = 2062
\(\text{Probability}=\frac{2062}{2400}=\frac{1031}{1200}\)

Q6. 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.

Solution:
Total number of students = 90

(i) \(\text{Probability}=\frac{7}{90}\)

(ii) \(\text{Probability}=\frac{23}{90}\)

Q7. To know the opinion of the students about the subject statistics, a survey of 200 students was conducted.

Solution:
Total number of students = 200

(i) \(\text{Probability}=\frac{135}{200}=\frac{27}{40}\)

(ii) \(\text{Probability}=\frac{65}{200}=\frac{13}{40}\)

Q8. 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 0.5 km from her place of work?

Solution:
Total number of engineers = 40

(i) \(\text{Probability}=\frac{9}{40}\)

(ii) \(\text{Probability}=\frac{31}{40}\)

(iii) \(\text{Probability}=\frac{0}{40}=0\)

Q9. Activity: Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval in front of your school gate.

Solution: This is an activity to be performed by students.

Q10. Activity: Ask all the students in your class to write a 3-digit number. Choose any student at random. What is the probability that the number written is divisible by 3?

Solution: This is an activity to be performed by students.

Q11. 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.

Solution:
Total number of bags = 11
Number of bags containing more than 5 kg flour = 7

\(
\text{Probability}
=\frac{7}{11}
\)

Q12. 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 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.

Solution:
Total number of days = 30
Number of favourable days = 2

\(
\text{Probability}
=\frac{2}{30}
=\frac{1}{15}
\)

Q13. 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.

Solution:
Total number of students = 30
Number of students with blood group AB = 3

\(
\text{Probability}
=\frac{3}{30}
=\frac{1}{10}
\)