5 cards drawn at random from a standard deck find the probability that all the cards are face cards
5 cards drawn at random from a standard deck. find the probability that all the cards are face cards
There are 12 face cards in a standard deck (4 jacks, 4 queens, and 4 kings). There are 52 cards in total.
The probability of drawing a face card on the first draw is 12/52, or 3/13.
Since we are drawing without replacement, there are only 51 cards left for the second draw. The probability of drawing another face card on the second draw is now 11/51.
Similarly, the probability of drawing a face card on the third draw is 10/50, the probability on the fourth draw is 9/49, and the probability on the fifth draw is 8/48.
To find the probability of all 5 cards drawn being face cards, we need to multiply the probabilities of each draw together:
(3/13) x (11/51) x (10/50) x (9/49) x (8/48) = 0.0000185
Therefore, the probability of drawing all 5 face cards is approximately 0.00185%, or about 1 in 54,097.