## Chapter 15 Probability Ex 15.1

**Question 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:**

**Question 2.**
**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:**

**Question 3.** **In a particular section of class IX, 40 students were asked about the month 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.** **Solution:**

**Question 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.** **Solution:**

**Question 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 ₹ 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.** **Solution:**

Total number of families selected by the organisation, n(S) = 2400

(i) The number of families earning ₹ 10000-13000 per month and owing exactly 2 vehicles, n(E_{1}) = 29

(ii) The number of families earning ₹ 16000 or more per month and owing exactly 1 vehicle, n(E_{2}) = 579

(iii) The number of families earning less than ₹ 7000 per month and does not own any vehicle, n(E_{3}) = 10

(iv) The number of families earning ₹ 13000-16000 per month and owing more than 2 vehicles, n(E_{4}) = 25

(v) The number of families owing not more than 1 vehicle,

n(E_{5}) = (10 + 1 + 2 + 1) + (160 + 305 + 535 + 469 + 579)

=14 + 2048 = 2062

**Question 6.** **A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows** **0-20, 20 – 30, …, 60 – 70, 70 – 100. Then she formed 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 marks 60 or above.** **Solution:**

**Question 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.** **Solution:**

Total number of students, n(S) = 200

(i) The number of students who like Statistics, n(E) = 135

(ii) The number of students who does not like Statistics, n(F) = 65

∴ The probability, that the student does not like Statistics

**Question 8.** **The distance (in km) of 40 engineers from their residence to their place of work were found as follows**

**Question 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?** **Solution:**

After observing in front of the school gate in time interval 6:30 to 7:30 am respective frequencies of different types of vehicles are .

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

**Question 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.** **Solution:**

**Question 12.** **A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows**

**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.** **Solution:**

Now, we prepare a frequency distribution table

The total number of days for data, to prepare sulphur dioxide, n(S) = 30

The frequency of the sulphur dioxide in the interval 0.12-0.16, n(E) = 2

**Question 13.** **The blood groups of 30 students of class VIII are recorded as follows** **A, B, 0, 0, AB, 0, A, 0, B, A, 0, B, A, 0, 0, A, AB, 0, A, A, 0, 0, AB, B, A, B, 0** **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:**