I have this statement:
A box contains 4 socks, brown, yellow, green and purple. The game consists of extracting one by one the socks without replacement. If the first one comes out coffee player wins $500$, if the second sock goes coffee the player wins $200$, if in none of the previous attempts is removed the coffee colored sock, loses $400$, What is the expected value in this game?
My attempt:
The probability that I get the brown sock on the first extraction is: $1/4$
Now, if in the first extraction I did not obtain the coffee, then I will have 3 remaining socks in the second extraction, of which $1$ is coffee, so the probability of obtaining it in the second extraction is: $1/3$
And the probabilty of loss is equal to: loss in the first and lost in the second, that is: $3/4 * 2/3 = 1/2$
Therefore, $E(X) = 500/4 +200/3 -400/2 = -25/3$, but the correct answer must be $-25$ and i don't know what is wrong with my development. Thanks in advance.
The probability of getting the brown on the second extraction is not $\frac{1}{3}$, but rather $\frac{3}{4}\times\frac{1}{3}$, as you first have to miss to draw it. That should fix your problem.