An urn contains three red balls, five white balls, and two black balls. Three balls are drawn from the urn at random without replacement. For each red ball drawn, you win $10, and for each black ball drawn, you lose $15. Let X represent your net winnings.
Compute E(X), your expected net winnings.
E(X) = ?

Question

An urn contains three red balls, five white balls, and two black balls. Three balls are drawn from the urn at random without replacement. For each red ball drawn, you win $10, and for each black ball drawn, you lose $15. Let X represent your net winnings.
Compute E(X), your expected net winnings.
E(X) = ?

anonymous · Answer

$$\mathbb{E}(X)=\sum_{\text{all balls}}(\text{probability of getting certain color})(\text{earnings/losses})$$

anonymous · Answer

So what's the probability of drawing a red ball? a white ball? a black ball? How much money do you earn/lose for each color?

anonymous · Answer

red ball probability is 3 out of 10   earn 10$
white ball of 5 out of 10                  0
black ball is 2 out of 10                  loose 15

anonymous · Answer

E(x)= 10(3/10) + 0(5/10) + -15(2/10)
      =      3        +     0      +   -3
      =   0
is this right?

anonymous · Answer

Yes