Answer to Question #130023 in Statistics and Probability for Ujjwal Aggarwal

Question

2 men M1 and M2 and 3 women W1, W2 and W3 are trying for promotion in a firm to a single post which is vacant. Those of the same sex have equal probabilities of getting promotion but each man is twice as likely to get the promotion as any woman.

1.) Find the probability that woman gets the promotion

2.) If M2 and W2 are couple, find the probability that one of them gets the promotion

Answer 1

Let p₁ be the probability that a woman gets the promotion,

and let p₂ be the probability that a man gets the promotion.

Then by conditon

3p₁+2p₂=1

and p₂=2p_1.

So, 3p₁+4p₁=1

7p₁=1

p₁=1/7, p₂=2/7.

The probability that a woman gets the promotion is equal to 1/7.

The probability that one of W₂ or M₂ gets the promotion is equal to p₁+p₂:

p₁+p₂=1/7+2/7=3/7

So, the probability that one of W₂ or M₂ gets the promotion is equal to 3/7.