Suppose you pay $5 to the dealer, who then shuffles a deck of cards and
deals six of them. You receive $3 for every diamond.
(i) Find the probability of winning (net) some money.
(ii) Compute the expected value and standard deviation of your (total) net win in one round of
this game,
(iii) and in 10 independent rounds of this game.
(iv) What is the probability of winning some money (net, in total) after 10 independent rounds?
Solution
(i) prob of winning some money= 1- prob of winning no money =1- prob of getting
no diamonds in 6 cards =1- (39/52) * (38/51)* (37/50) * (36/49) * (35/48) * (34/47) (ii) prob of
getting, say 2 diamonds is =(39C4) * (13C2)/ (52C6) (ways of drawing 4 non-diamonds (out of
39 cards) * no. of ways getting 2 diamonds ( among 13) using these probabilities expected gain
can be obtained