Question

Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is twice as likely to be selected as B, and B and C are given about the same chance of being selected, while C is twice as likely to be selected as D, what are the probabilities that

(a) C will be selected?

(b) A will not be selected?

Answer 1

Given that A is twice as likely to be selected as B

i.e. P(A) = 2 P(B) …(i)

and C is twice as likely to be selected as D

i.e. P(C) = 2P(D) …(ii)

Now, B and C are given about the same chance

∴ P(B) = P(C) …(iii)

Since, sum of all probabilities = 1

∴ P(A) + P(B) + P(C) + P(D) = 1

⇒ P(A) + P(B) + P(B) + P(D) = 1 [from (iii)]

(a) P(C will be selected) = P(C)

= P(B) [from(iii)]

(b) P(A will not be selected) = P(A’)

= 1 – P(A)

[By complement Rule]