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Question
Given below is the frequency distribution of wages (in Rs) of 30 workers in a certain factory:
| Wages (in Rs) | 110-130 | 130-150 | 150-170 | 170-190 | 190-210 | 210-230 | 230-250 |
| No. of workers | 3 | 4 | 5 | 6 | 5 | 4 | 3 |
A worker is selected at random. Find the probability that his wages are:
(i) less than Rs 150
(ii) at least Rs 210
(iii) more than or equal to 150 but less than Rs 210.
Solution
The total number of trials is 30.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by P ( A ) and is given by
` P (A) = m/n`
(i) Let A1 be the event that the wages of a worker is less than Rs 150.
The number of times A1 happens is 3+4=7 .
Therefore, we have ` P(A_1 )= 7/30` .
(ii) Let A2 be the event that the wages of a worker is atleast Rs 210.
The number of times A2 happens is 4+3=7 .
Therefore, we have` P(A_2)= 7/30` .
(iii) Let A3 be the event that the wages of a worker is more than or equal to Rs 150 but less than Rs 210.
The number of times A3 happens is 5 + 6 + 5 = 16 .
Therefore, we have
` P(A_3 )= 16/30`
`=8/15`
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