Question

A total of 3 cards are chosen at random, without replacing them, from a standard deck of 52 playing cards. What is the probability of choosing 3 king cards?

Answer 1

1/5525 ≈ 0.018%

Explanation:

There are 4 kings in a standard deck of 52 cards.

The probability that the first card is a king is 4/52.

The probability that the second card is also a king is 3/51 (the first king isn't replaced, so there's one less king and one less card in the deck).

The probability that the third card is a king is 2/50.

The probability of choosing 3 king cards is therefore:

P = (4/52) (3/51) (2/50)

P = (1/13) (1/17) (1/25)

P = 1/5525

P ≈ 0.018%