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Solution - Probability - an Experimental Approach

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Question

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.

Solution

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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
Total30

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
Frequency23727728

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.

53102025111371231
1910121718113217162
7978351215183
121429615157612

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
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