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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 will not be selected?
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Solution
Given that A is twice as likely to be selected as B
i.e. P(A) = 2P(B)
And C is twice as likely to be selected as D
∴ P(C) = 2P(D)
⇒ P(B) = 2P(D)
⇒ `(P(A))/2` = 2P(D)
⇒ P(D) = `1/4`P(A)
Now B and C are given about the same chance
∴ P(B) = P(C)
Since, sum of all probabilities = 1
∴ P(A) + P(B) + P(C) + P(D) = 1
⇒ `P(A) + (P(A))/2 + (P(A))/2 + (P(A))/4` = 1
⇒ 4P(A) + 2P(A) + 2P(A) + P(A) = 4
⇒ 9P(A) = 4
⇒ P(A) = `4/9`
P(A will not be selected) = P(A') = 1 – P(A)
= `1 - 4/9`
= `5/9`
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