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  • 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

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?

Answers (1)

Given:

A is twice likely to be selected as B, P(A) = 2 P(B)

& C is twice likely to be selected as D, P(C) = 2 P(D)

It is given that B & C have about the same chance

Thus, P(B) = P(C)

Now, sum of all probabilities is 1,

Thus,

P(A) + P(B) + P(C) + P(D) = 1

P(A) + P(B) + P(B) + P(D) = 1

Thus,

P(A) + P(A)/2 + P(A)/2 + P(C)/2 = 1

[2 P(A) + P(A) + P(A) + P(B)] /2 = 1

4 P(A) + P(A) / 2 = 2

[8 P(A) + P(A)] / 2 = 2

9 P(A) = 4

P(A) = 4/9

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

                                    = P (B)

                                    = 4/9 x ½

                                    = 2/9

(b) P (A will not be selected) = P (A’)

                                    = 1 – P (A)    ……. (by complement rule)

                                    = 1 – 4/9

                                    = 9-4/ 9

                                    = 5 / 9

Posted by

infoexpert22

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