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.

Answer 1

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`