Question

For the vacancy advertised in the newspaper, 3000 candidates submitted their applications. From the data it was revealed that two third of the total applicants were females and other were males. The selection for the job was done through a written test. The performance of the applicants indicates that the probability of a male getting a distinction in written test is 0.4 and that a female gettinga distinction is 0.35. Find the probability that the candidate chosen at random will have a distinction in the written test.

Answer 1

Given: Total candidates = 3000

No. of females = `2/3 xx 3000`

= 2000

No. of males = `1/3 xx 3000`

= 1000

E₁: Chosen candidate is female

E₂: Chosen candidate is male

A: Getting a distinction written test

∴ `P(E_1) = 2/3`,

`P(E_2) = 1/3`

P(A/E₁) = 0.35

P(A/E₂) = 0.4

From the total probability theorem

P(A) = P(E₁) P(A/E₁) + P(E₂) P(A/E₂)

= `2/3 xx 0.35 + 1/3 xx 0.4` 

= `2/3 xx 35/100 + 1/3 xx 4/10` 

= `(70/300 + 4/30)`

= `((70 + 40)/300)`

= `110/300`

= `11/30`