Question

Q19. Consider an ordinary 52-card North American playing deck (4 suits, 13 cards in each suit).

a) How many different 5−card poker hands can be drawn from the deck?

b) How many different 13−card bridge hands can be drawn from the deck?

c) What is the probability of an all-spade 5−card poker hand?

d) What is the probability of a flush (5−cards from the same suit)?

e) What is the probability that a 5−card poker hand contains exactly 3 Kings and 2 Queens?

f) What is the probability that a 5−card poker hand contains exactly 2 Kings, 2 Queens, and 1 Jack?

If possible please show your work! I'm really struggling with this question.

Answer 1

We would be looking at the first 4 parts here as:

a) As all 52 cards are distinct here, the number of different 5 card poker hands is computed here as:

= Number of ways to select 5 cards from 52 cards

b) The number of 13 card hands here is computed as:

= Number of ways to select 13 cards from 52 cards

c) The probability of getting an all spade 5 card poker hand is computed here as:

= Number of ways to select 5 spades from 13 spades / Total poker hands possible

d) The probability of a flush hand is computed here as:

= Number of ways to get all spade / hearts / clubs or diamond cards