Originally Posted by

**chrisc** Suppose you pay $5 to the dealer, who then shuffles a deck of cards and

turns over the top six of them. You receive $3 for every diamond.

**(a)** Find the probability of winning (net) some money.

**(b)** Compute the expected value and standard deviation of your (total)

net win in one round of this game,

**(c)** and in 15 independent rounds of this game.

__Answers:__

**(a)** I calculated the probability of getting 0 diamonds and 1 diamond, and subtracted that from 1

Pr(0D) = (39C6)/(52C6) = 0.1603

Pr(1D) = (13C1)(39C5)/(52C6) = 0.3677

1 - Pr(0D) - Pr(1D) = 0.4720

**(b)** For this I calculated the probability of 0, 1, 2, 3, 4, 5 6 diamond scenerios (similar to above), but then I multiplied each probability the the net loss or winnings that would occur.

I got E(X) = -0.8155

which makes sense since the probability of winning is less than 1/2

However, I am having a hard time finding out the process to get the standard deviation in this case. Any help is appreciated.

and for part **(c)**, would the answer be the same as in part (b)? although there are 15 games, they are still independent of each other.