SOLUTION: A 5-card hand is dealt from a deck of 52 cards. What is the probability that a.) none are queens? b.) all are queens?

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Question 619298: A 5-card hand is dealt from a deck of 52 cards. What is the probability that
a.) none are queens?
b.) all are queens?
Found 2 solutions by sophxmai, richard1234:
Answer by sophxmai(62) About Me  (Show Source):
You can put this solution on YOUR website!
There are only 4 queens in a deck of cards.
P(a)= probability that event A occurs
= (total number of desired outcomes)/(total number of possible outcomes)
Use combinatorics.

The total number of possible outcomes in a) and b) is
52C5 = 2598960

The total number of desired outcomes in a) is
48C5 = 1712304
It's 48 because you don't want any queens, and there are 4 queens in a deck of 52

The total number of desired outcomes in b) is
0 because there are only 4 queens in a deck of 52, but you want your 5 card hand to be all queens.

So
a)P(no queens in a 5 card hand)=1712304/2598960=0.659
b)P(all queens in a 5 card hand)=0/2598960=0

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
a) There are 52C5 total hands, and 48C5 do not contain queens. Therefore the probability is



b) Zero. Only four queens in a deck