Q1) Probability of a flush.  Poker player holds flush when all 5 cards in hand belong to same suit (clubs, diamonds, hearts, or spades). We will find probability of flush when 5 cards are dealt. Remember that 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. Determine the probability that first card dealt is a spade? What conditional probability that second card is a spade, given that first is a spade? How many cards remain? How many of these are spades?

b) Continue to count remaining cards to determine conditional probabilities of spade on third, fourth, and fifth card, given in each case that all earlier cards are spades.

c) Probability of being dealt 5 spades is product of 5 probabilities you have found. Why? Find out the probability?

d) Probability of being dealt 5 hearts or 5 diamonds or 5 clubs is same as probability of being dealt 5 spades. Determine the probability of being dealt a flush?