We know that a basketball player is moving from Europe to USA. He can go to one of the teams $A,B,C,D,E$ with probabilities:

$P(A) = \frac{1}{2}$, $P(B) = \frac{1}{4}$, $P(C) = \frac{1}{8}$, $P(D) = \frac{1}{16}$, $P(E) = \frac{1}{16}$.

Meanwhile a journalist found out who bought the player and wants to sell the name to a newspaper. After a while team B decides to buy another player thus making obvious that they are not going to buy our player. How much value does the journalist's news lose?

Considering that the information of an event a is defined as:

$i = \log_\frac{1}{2} P(a)$

I would say that the value lost by the news is equal to the information carried by team B so:

$i = \log_\frac{1}{2} P(B)= \log_\frac{1}{2} \frac{1}{4} = 2$

I would like to know if the solution is right


1 Answer 1


Your solution is wrong. For one thing, the information given is not that the player in question was bought by $B$, but that he was not bought by $B$.

The safe way is to compute the information before and after, which is to say: the entropy.

After the buying, the probabilities change. $p^*_B=0$, and the remainder are the same, but scaled so that their sum is 1. $p_i^* = p_i /(1-p_B)=p_i \,4/3$


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