Find the probability of being dealt a flush all five cards t

Find the probability of being dealt a flush (all five cards the same suit) in a 5-card hand of poker from a standard deck of 52 cards.

Solution

Since there are 4 suits in a set of card, there can be 4 deal of a flush.

Therefore, P(a flush) = P(all five cards the same suit) x 4

Now, P(all five cards the same suit) = Probability of a card from that suit at 1st draw from 52 cards x Probability of a card from that suit at 2nd draw from the remaining 51 cards x Probability of a card from that suit at 3rd draw from the remaining 50 cards x Probability of a card from that suit at 4th draw from the remaining 49 cards x Probability of a card from that suit at 5th draw from the remaining 48 cards= 13/52 x 12/51 x 11/50 x 10/49 x 9/48

Therefore, P(a flush) = 13/52 x 12/51 x 11/50 x 10/49 x 9/48 x 4 = 0.00198