Question 235056: five cards are dealt, what is the probability that the fifth one is a king
Answer by solver91311(5072)   (Show Source):
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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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