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Question

There are n urns each containing n+1 balls such that the ith um contains i white balls and (n+1i) red balls. Let ui be the event of selecting ith urn, i=1,2,3, n and w denotes the event of getting a white ball.

If n is even and E denotes the event of choosing even numbered um (P(ui)=1n), then the value of P(w/E) is

A
n+22n+1
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B
n+22(n+1)
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C
nn+1
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D
1n+1
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Solution

The correct option is B n+22(n+1)
given that n is even
n(wE)= event of getting white balls from even numbered urn
=2+4+6+......+n=2(1+2+3+....+n2)=2×(n/2)(n/2+1)2=n4(n+2)
n(E)= event of selecting even numbered urn
= no. of balls in each urn × number of even numbered urns
=(n+1)×n2
P(wE)=n(n+2)/4n(n+1)/2=n+22(n+1)

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