Four candidates A, B, C, D have applied for the assignment ot 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 probability that (i) C will be selected ? (ii) A will not be selected?

Explanation

It is given that A is twice as likely to be selected as B.
`therefore` P(A) = 2P(B)
B and C have same chances of being selected.
`therefore` P(B) = P(C )
C is twice as likely to be selected as D.
`therefore` P(C ) = 2P(D)
So, P(B) = 2P(D)
`implies P(A) = 4P(D) implies P(D) = (P(A))/(4)`
Sum of all probabilities = 1
`therefore P(A) + P(B) + P(C ) + P(D) = 1`
`implies P(A) + (P(A))/(2) + (P(A))/(2) + (P(A))/(4) = 1`
`implies (4P(A) + 2P(A) + 2P(A) + P(A))/(2) = 1`
implies `implies 9P(A) = 4 implies P(A) = (4)/(9)`
(i) P(C will be selected) = `P(C) = (P(A))/(2) = (4)/(9xx2) = (2)/(9)`
(ii) P(A will not be selected) = P (B or C or D will be selected)
= P(B) + P(C ) + P(D)
`=(P(A))/(2) + (P(A))/(2) + (P(A))/(4) = (5)/(9)`