CBSE - Probability

In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

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.

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.

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.

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 Rs10000 – 13000 per month and owning exactly 2 vehicles.
(ii) earning Rs16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than Rs7000 per month and does not own any vehicle.
(iv) earning Rs13000 – 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle. 

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.

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.

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

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?

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.

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 frequency distribution of the data obtained for 30 days is as follows:  

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 blood groups of 30 students of class VIII are given in the following frequency distribution table:  

Use this table to determine the probability that a student of this class, selected at random, has blood group AB.