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December 25th, 2016, 10:42 AM   #1
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Information Theory exercise

Anyone could please tell me how to solve this exercise?

Let there be $\displaystyle n+1$ boxes labeled $\displaystyle \omega=1,2,...,n$. One of the boxes contains a
prize, the others are empty. The probability $\displaystyle p_0$ that the prize is in $\displaystyle \omega=0$ is much
larger than the probability that it is in any other box: $\displaystyle p_0>>p_{\omega>0}$ and we take
$\displaystyle p_{\omega>0}=\frac{1-p_0}{n}$ for simplicity. Note that, if $\displaystyle n$ is large, $\displaystyle p_0$ can nonetheless be also small.
There are two possible options:

1) open the box $\displaystyle \omega=0$;
2) open simultaneously all boxes $\displaystyle \omega>\frac{n}{2}$ (imagine $\displaystyle n$ is even).
Which one is the most convenient? Which one conveys most information on where the prize actually is?
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