Expected Value Question

Question

A box contains 4 red and 6 green balls. Two balls are drawn. You receive $10 if both are red and you pay $1 otherwise. What are your expected earnings?

Answer 1

The probability that both are red: (4 choose 2)/(10 choose 2) = 2/15

Therefore the probability that they're not both red is 1 - 2/15 = 13/15

In the event that they're both red (2/15ths of the time), you receive $10, in the event that they're not both red (13/15ths of the time), you lose $1.

(2/15)(10) + (13/15)(-1) = 7/15.

That means that in the long run, you expect to make an average of 46.67 cents every time you play this game.

Answer 2