Consider a game of poker being played with a standard 52-card deck (four suits, each of which has 13 different denominations of cards). At a certain point in the game, six cards have been exposed. Of the six, four are diamonds. Your opponent makes a bet of $20, and you must decide whether to call the bet. If you do call the bet, you will receive one more card. If that final card turns out to be another diamond, you will win $100. If not, you will lose the hand as well as the $20 you called in order to receive the final card. On the other hand, if you do not call the bet, the hand ends immediately, your opponent wins, and you neither win nor lose any more money.
a. Specific the probability distribution for X = expected winnings.
b. Find the expected value of X. Based on the expected value, should you call the $20 bet and receive one more card or not call the bet?