You draw five cards from a deck containing all thirteen cards of a single suit.

Question

You draw five cards from a deck containing all thirteen cards of a single suit.

(a) What is the probability of drawing a flush? (That is, all cards having the same suit.)

(b) What is the probability of drawing the 2, 3, 4, 5, and 6?

(c) What is the probability of drawing a straight? (That is, five cards in a row, where the Jack is treated as an 11, Queen is 12, King is 13, and Ace can be either 1 or 14 but not both. 10JQKA is a straight, but JQKA2 is not a straight.)

(d) What is the probability of not drawing a straight?

Explanation / Answer

a) As there are 13 cards in a deck from a single suit only, any 5 cards drawn are from the same suit hence the flush.
Hence required probability = 1

b) 5 cards from a deck of 13 cards can be drawn in 13C5 ways.
Drawing 2,3,4,5 and 6 can be done in only 1 way
hence required probability = 1 / 13C5 = 1/1287

c)
If ace is considered as 1, there are 9 straight hands.
If ace is considered as 14, there are 9 straight hands.
There are 8 common hands in both. Hence only 10 unique hands are possible
Hence required probability is 10/1287

d)
Probability of not drawing straight = 1 - 10/1287 = 1277/1287

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