Make a tree diagram for the results of the two serves and the outcome (win or lose) of the point. What is the probability that the five cards drawn all belong to the same suit? (d) The probability of drawing five hearts or five diamonds or five clubs is the same as the probability of drawing five spades. (c) The probability of drawing five spades in succession from the top of the deck is the product of the five probabilities you have found.

(b) Continue to count the remaining cards to find the conditional probabilities of a spade for the third, the fourth, and the fifth card drawn, given in each case that all previous cards are spades. What is the probability that the first card drawn is a spade? What is the conditional probability that the second card drawn is a spade, given that the first is a spade? (Hint: How many cards remain? How many of these are spades?) Remember that a deck contains 52 cards, 13 of each suit and that when the deck is well shuffled, each card drawn is equally likely to be any of those that remain in the deck. We will find the probability of a flush when five cards are drawn in succession from the top of the deck. A poker player holds a flush when all five cards in the hand belong to the same suit (clubs, diamonds, hearts, or spades).

No spades in hand poker