A standard deck of cards is made up of four suits with 13 cards in each suit (total of 52 cards). If we randomly sample five cards from a standard poker deck, find the probability that all five cards selected are clubs.
13/51
13/52
13/52 * 12/51 * 11/50 * 10/49 * 9/48
C(13,5) = 13!/(3!*10!) = 154440/120 = 1287
To find the probability that all five cards selected are clubs, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Since we are sampling five cards from a standard deck of 52 cards, there are a total of (52 choose 5) possible outcomes. This can be calculated using combinatorics formula: C(52, 5) = 52! / (5! * (52 - 5)!) = 2598960.
Number of favorable outcomes:
There are 13 clubs in a deck of cards. Since we are sampling without replacement, the probability changes after each draw. For the first card, there are 13 clubs out of 52 total cards. For the second card, there are 12 clubs out of the remaining 51 cards. Similarly, for the third, fourth, and fifth cards, there are 11, 10, and 9 clubs respectively, out of the remaining cards. Therefore, the number of favorable outcomes is (13 choose 5) = 13! / (5! * (13 - 5)!) = 1287.
Now, we can find the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1287 / 2598960
≈ 0.000495
So, the probability that all five cards selected are clubs is approximately 0.000495 or 0.0495%.