Question

Question #ce6b5

Answer 1

`13/52 * 12/51*11/50*10/49*9/48`.

Explanation:

Provided that this is from a standard 52 card deck, without jokers included, and without replacement, then this would be. Shown as follows:

`13/52 * 12/51*11/50*10/49*9/48`

There are 13 clubs in a standard 52 card deck, so the first fraction shown is the probability of the first card being a club. For the second card, if there is no replacement, there are 12 clubs remaining in a now 51 card deck, so our probability of the second card being a club is the second fraction. This pattern continues for the third, fourth, and fifth cards.

Note that if we are replacing the card, that is shuffling the card back into the deck, then the probability of any individual card being a club is simply `13/52=1/4`, meaning the probability of all 5 draws yielding a club is `(1/4)^5`

Answer 2

`33/66640`

Explanation:

This is for dealing out 5 clubs without replacement from a standard 52 card deck. This would seem the most obvious situation. The probability of the first card being a club is:

`13/52` This leaves 12 clubs and total of 51 cards.

Probability of second card being a club:

`12/51` This pattern continues until all five cards are dealt:

`13/52 ,12/51 , 11/50 , 10/49 , 9/48`

These have to be multiplied together.

`13/52 * 12/51 * 11/50 * 10/49 * 9/48 = 33/66640`