Probability

Exercise 1

1.    In a cricket match a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that he will

(i) Hit a boundary in the next ball.

(ii) Not hit boundary in the next ball.

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

No. of girls in a family      No. of families

2                                           475

1                                           814

0                                          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.

3.   In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:

Find the probability that a student of the class was born in August.

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

Outcomes                            Frequency

    3 heads                                        23

    2 heads                                        72

    1 head                                          77

    No head                                      28

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


5.    An organization 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: earning Rs. 10000 – 13000 per month and owning exactly 2 vehicles.

(i) Earning Rs. 16000 or more per month and owning exactly 1 vehicle.

(ii) Earning less than Rs. 7000 per month and does not own any vehicle.

(iii) Earning Rs. 13000 – 16000 per month and owning more than 2 vehicles.

(iv) Not more than 1 vehicle.

6.    A teacher analyses the performance of two sections of students in a mathematics test of 100 marks given in the following table:

(i) Find the probability that a student obtained less than 20% in the mathematics test.

(ii) Find the probability that a student obtained 60 or above.


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:

Opinion               No. of students

   likes                                135

   dislikes                           65

Find the probability that a student chosen at random:

(i) likes statistics  (ii) dislikes it.

8.    Refer Q.2, Exercise 14.2. What is the empirical probability than 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  km from her place of work?

9.    Activity: Note the frequency of two wheelers, three wheelers and four wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two wheeler.

10.  Activity: Ask all the students in your class room to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by him is divisible by 3, if the sum of its digits is divisible by 3.

11.  Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of four (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.

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.

13.  In Q.1, Exercise 14.1 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.