SOLUTION: five cards are dealt, what is the probability that the fifth one is a king

Question 235056: five cards are dealt, what is the probability that the fifth one is a king
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Depends on whether you can see the value of the first four or not.

If you don't know the value of the first four cards, then there are 4 kings in 52 cards, or

.

On the other hand, if you can see the first four cards, then the denominator of the fraction changes from 52 to 48, that is 52 minus the 4 cards you can see leaving you 48 cards you don't know about. The numerator is a little more complicated.

The numerator of the probability depends on the number of kings that appear in the first 4 cards. Quite obviously, if the first 4 cards are themselves kings, then the probability that the fifth card will be a king is zero -- because there aren't any left.

So, let

represent the number of kings that appear in the first four cards, then the probability that the fifth card is a king is calculated by the following:

,

and you can say:

John

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