The probability of a flush. A poker player holds a flush when all 5 cards in thehand

Chapter 0, Problem 12.12

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The probability of a flush. A poker player holds a flush when all 5 cards in thehand belong to the same suit (clubs, diamonds, hearts, or spades). We will find theprobability of a flush when 5 cards are dealt. Remember that a deck contains52 cards, 13 of each suit, and that when the deck is well shuffled, each card dealtis equally likely to be any of those that remain in the deck.(a) Concentrate on spades. What is the probability that the first card dealt is aspade? What is the conditional probability that the second card is a spade, giventhat the first is a spade? (Hint: How many cards remain? How many of these arespades?)(b) Continue to count the remaining cards to find the conditional probabilitiesof a spade on the third, the fourth, and the fifth card, given in each case that allprevious cards are spades.(c) The probability of being dealt 5 spades is the product of the 5 probabilitiesyou have found. Why? What is this probability?(d) The probability of being dealt 5 hearts or 5 diamonds or 5 clubs is the same asthe probability of being dealt 5 spades. What is the probability of being dealt aflush?