3. A casino owner designs a game in which a regular deck of cards is shuffled and a

gambler is allowed to select any card at random.

If he selects an ace he wins $10.

If he selects a face card (i.e. J, Q, or K) he wins $5.

If he selects any other card he wins $1.

(a) Assuming the casino owner wants at least to break even, what is the minimum

value he should charge the gambler to play this game?

(b) What is the standard deviation for the gambler's winnings?

(c) What is the probability that the gambler wins more than $1?

(d) Suppose a gambler plays the game twice. What is the probability that his total

winnings exceed $2?