Question

A poker hand (5 cards) is dealt from a well shuffled deck of cards. Find (a). The chance that the cards are all diamonds; (b). The chance that the cards are all of the same suits.

Answer 1

There are 13 diamond cards (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A)


There are 13 C 5 = 1287 ways to deal out 5 diamond cards.


There are 52 C 5 = 2598960 ways to deal out 5 cards of any type


So the probability of getting 5 diamond cards is 1287/2598960 = 33/66640 = 0.000495

Answer 2

Thank you so much, I appreciate; but what about the B part of the question?

Answer 3

When you get the first card, it dictates which suit you're dealing with

Answer 4

So let's say the first card is a 2 of hearts

Answer 5

The other four cards must be hearts (to get what you want)

Answer 6

There are 12 heart cards left

There are 4 slots left (in the hand)

So there are 12 C 4 = 495 ways to finish up the hand you want

There are 51 C 4 = 249900 hands total (after you make your first draw) of any card combo

So the probability is 495/249900 = 33/16660 = 0.00198079

Answer 7

This probability is slightly higher than the one found in part a)

So it's more likely to draw 5 cards of the same suit than to just draw all 5 diamond cards. This makes sense because there are more cases in part b), leading to a higher probability.

Answer 8

Thank you so much.

Answer 9

np