If you are dealt 4 cards from a shuffled deck of 52​ cards, find the probability that all 4 cards are clubs.

Answer 1

There are 13 clubs in the deck of 52 cards. That makes the probability of the first card being a club 13/52, which reduces to 1/4.

For the second card, there are 12 clubs in the 51 that remain, so the probability it's a club is 12/51, or 4/17.

There are now 11 clubs in the remaining 50, so the probability the third card is a club is 11/50.

Finally, you have 10 clubs out of 49 cards, making the probability that the 4th card is a club is 10/49.

To get the probability of this whole scenario, just multiply the four fractions (and simplify).

Answer 2

The probability that the first card picked is a club is 13/52 because there are 13 clubs and 52 total cards. The probability that the second card picked is a club will then be 12/51 and the third will be 11/50 and the forth will be 10/49. So the probability that all 4 cards will be clubs is 13/52 • 12/51 • 11/50 • 10/49 = 17160/6497400 which can be reduced to 11/4165, or, as a percentage, that would be 0.264%