Question

Three persons A, B and C apply for a job a manager in a private company. Chances of their selection are in the ratio 1:2:4. The probability that A, B and C can introduce chances to increase the profits of a company are 0.8, 0.5 and 0.3 respectively. If increase in the profit does not take place, find the probability that it is due to the appointment of A.

Answer 1

Let E₁ = Person A gets the job

E₂ = Person B gets the job

E₃ = Person C gets the job

A = No change takes place

The changes of selection of A, B and C are in the ratio 1:2:4

Hence, P(E₁) = `1/7`, P(E₂) = `2/7`, P(E₃) = `4/7`

Also, given `P(A/E_1) = 0.2 = 2/10, P(A/E_2) = 0.5 = 5/10`

And `P(A/E_3) = 0.7 = 7/10`

Required probability is `P(E_1/A) = (P(A/E_1).P(E_1))/(P(A/E_1).P(E_1) + P(A/E_2).P(E_2) + P(A/E_3).P(E_3))`

= `(2/10 xx 1/7)/(2/10 xx 1/7 + 5/10 xx 2/7 + 7/10 xx 4/7)`

= `(2/70)/(2/70 + 10/70 + 28/70)`

= `2/40`

= `1/20`

∴ If no change takes palace, the probability that it is due to appointment of person A is `1/20`.