Question

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?

Answer 1

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.

Answer 2

`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%`