Choose 2 cards from a standard 52 card card, in succession and without replacement. What is the probability that the second card is a king given that the first card is a face card?

2 Answers
Gió
Aug 2, 2017

I tried this...but I am not sure I interpreted the problem correctly:

Explanation:

After you pick the first card there will be left #51# cards in the pack.
The second pick will deal with the remaining #51# possible events and the events associated in picking one of the #4# kings. The problem is that in the first pick you may have picked a king...
Now:

if the first card was a face card different from a king we get that there are still #4# kings in the pack and so:

#p=4/51=0.00784# or #7.84~~7.8%# probability to get a king;

if the first card was a king we get that in the pack we have only #3# kings left, so:
#p=3/51=0.00588# or #5.88~~5.9%# probability to get a king.

EZ as pi
Aug 3, 2017

#11/663#

#1.66%#

Explanation:

We need to consider two scenarios:

The first card is a face card, not a king, and the second is a king

The first card is a king and the second card is a king.

#P(F,K) or P(K,K)#

#= (8/52 xx 4/51) + (4/52 xx3/51)#

#= 32/2652 +12/2652#

#=44/2652#

#=11/663#

Probabilities are usually given as a fraction.

As a percent this would be #1.66%#

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