Question

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

$IfP\left(u_i\right)=c$, where $c$ is a constant then $P\left(u_n/w\right)$ is equal to

• A. $\frac{2}{n+1}$
• B. $\frac{1}{n+1}$
• C. $\frac{n}{n+1}$
• D. $\frac{1}{2}$

Answer 1

Answer: (A)

$\frac{2}{n+1}$

$P\left(\frac{u_n}{w}\right)=\frac{c\left(\frac{n}{n+1}\right)}{c\left(\frac{\Sigma i}{(n+1}\right)}$

$=\frac{\frac{n}{n+1}}{\frac{n(n+1)}{2(n+1)}}$

$=\frac{2}{n+1}$