The probability of flush. A poker player holds flush when all 5 cards in hand belong to the same suit (clubs, diamonds, hearts, or spades). We will find out the probability of the flush when 5 cards are dealt. Remember that a deck contains 52 cards, 13 of each suit, and that when deck is well shuffled, each card dealt is equally likely to be any of those that remain in deck.
(a) Concentrate on spades. Find out the probability that the first card dealt is a spade? What conditional probability that the second card is a spade, given that the first is the spade? (Hint: How many cards remain? How many of these are spades? )
(b) Continue to count the remaining cards to find out the conditional probabilities of the spade on the third, the fourth, and the fifth card, given in each case that all previous cards are spades.
(c) The probability of being dealt five spades is the product of the five probabilities you have found. Why? What is this probability?
(d) The probability of being dealt 5 hearts or 5 diamonds or 5 clubs is same as the probability of being dealt 5 spades. Find out the probability of being dealt the flush?