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In Example 94, if `P(U_(i))=C`, where C is a constant, then `P(U_(n)//W)` is equal to

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In Example 94, if P(Ui)=C, where C is a constant, then P(Un/W) is equal to A. 2 n+1 B. 1 n+1 C. n n+1 D. 1 2 Select the correct answer from above options

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Correct Answer - A We have, P(Ui)=C,i=1,2,3,..,n ∴ n ∑ i=1 P(Ui)=1⇒ n ∑ i=1 C=1⇒C= 1 n ∴P(Ui)= 1 n ,i=1,2,3,..,n ∴P(Un/W)= P(Un∩W) P(W) ⇒P(Un/W)= P(Un∩W) ∑n i=1 (Ui∩W) ⇒P(UnRW)= P(Un)P(W/Un) ∑i=1nP(Ui)P(W/Ui) = 1 n × n n+1 ∑n i=1 C× 1 n+1 ⇒P(Un/W)= 1 C ∑n i=1 i = 1 1 n × n(n+1) 2 = 2 n+1

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