Solution - Probability - an Experimental Approach



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

Number of girls in a family210
Number of families475814211

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.


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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:-

Monthly income

(in Rs.)

Vehicles per family
012Above 2
Less than 700010160250
7000 – 100000305272
10000 – 130001535291
13000 – 1600024695925
16000 or more15798288

Suppose a family is chosen, find the probability that the family chosen is

(i) earning Rs 10000 − 13000 per month and owning exactly 2 vehicles.

(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs 7000 per month and does not own any vehicle.

(iv) earning Rs 13000 − 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.

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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:-

MarksNumber of students
0 - 207
20 - 3010
30 - 4010
40 - 5020
50 - 6020
60 - 7015
70 - above8
         Total                               90

(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.

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Concentration of SO2 (in ppm)Number of days (Frequency)
0.00 − 0.044
0.04 − 0.089
0.08 − 0.129
0.12 − 0.162
0.16 − 0.204
0.20 − 0.242

The above frequency distribution table represents 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.

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

Outcome3 heads2 heads1 headNo head

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

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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?What is the empirical probability that an engineer lives:

(ii) more than or equal to 7 km from her place of work?

(iii) within 1/2 km from her place of work?

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Solution for concept: Probability - an Experimental Approach. For the course 8th-10th CBSE