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Four candidates A, B, C, D have applied ...

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?

Text Solution

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It is given that A is twice as likely to be selected as D.
`P(A)=2P(B)`
`rArr " "(P(A))/(2)=P(B)`
while C is twice as likely to be selected as D.
`P(C)=2P(D)rArrP(B)=2P(D)`
`rArr " "(P(A))/(2)=2P(D)rArrP(D)=(P(A))/(4)`
B and C are given about the same chance of being selected.
`P(B)=P(C)`
`"Now" " ""sum of probability"=1`
`P(A)+P(B)+P(C)+P(D)=1`
`P(A)+(P(A))/(2)+P(A)/(2)+(P(A))/(4)=1`
`rArr " "(4P(A)+2P(A)+2P(A)+P(A))/(4)=1`
`rArr " "9P(A)=4rArrP(A)=(4)/(9)`
(i) `"P(C will be selected)"=P(C)=P(B)=(P(A))/(2)`
`=(4)/(9xx2) " "[becauseP(A)=(9)/(4)]`
`=(2)/(9)`
(ii) `"P(A will not be selected)"=P(A')=1-P(A)=1-(4)/(9)=(5)/(9)`
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