Question

If you are dealt 4 cards from a deck 52 find the probability that 4 cards are clubs

Answer 1

Explanation:

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

Explanation:

P(Clubs) = 13C4 // 52C4

The order doesn't matter in either case.

13 * 12 * 11 * 10

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52 * 51 * 50 * 49

P(4 cards all clubs) = 11/4165

P(4 cards all clubs) = 0.002641