Expert: Paul Klarreich - 5/26/2008

Question
You are dealt a 13 card bridge hand from a 52 card bridge deck.

a. What is the probability that you will be dealt exactly 5 hearts?

b. What is the probability that you will be dealt at least 2 hearts?

c. What is the probability that you will receive 5 hearts, 4 clubs, 2 diamonds, and 1 spade?

Answer
Questioner:   Joel
Category:  Advanced Math
Private:  No
 
Subject:  Probability
Question:  
.........................
Hi, Joel,

You are dealt a 13 card bridge hand from a 52 card bridge deck.

>> So the denominator is always C(52,13) in the rest -- I will just focus on the numerators.

a. What is the probability that you will be dealt exactly 5 hearts?

C(13,5) * C(39,8)


b. What is the probability that you will be dealt at least 2 hearts?

P(void) = C(39,13)
P(stiff) = C(13,1) * C(39,12)

Add those, then do 1 - probability.  Do this for any of these 'at least ... ' problems, not just for card combos.

c. What is the probability that you will receive 5 hearts, 4 clubs, 2 diamonds, and 1 spade?
 
C(13,5) * C(13,4) * C(13,2) * C(13,1)