If you are dealt 4 cards from a shuffled deck of 53 cards, find the probability that all 4 cards are picture cards.
A standard deck of playing cards has 52 cards, with 12 picture cards (4 kings, 4 queens, and 4 jacks). If you are dealt 4 cards from a deck of 53 cards, we can consider it as picking 4 cards from a deck of 52 cards and 1 additional joker card.
The total number of ways to choose 4 cards from 53 is given by the combination formula:
C(53, 4) = 53! / (4! * (53-4)!) = 53! / (4! * 49!) = (53 * 52 * 51 * 50) / (4 * 3 * 2 * 1) = 13,52,600
The number of ways to pick all 4 picture cards from the deck is given by the combination formula:
C(12, 4) = 12! / (4! * (12-4)!) = 12! / (4! * 8!) = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1) = 495
Therefore, the probability of pulling all 4 picture cards from a deck of 53 cards is:
P(all 4 picture cards) = C(12, 4) / C(53, 4) = 495 / 13,52,600 ≈ 0.00036607
So, the probability is approximately 0.00036607, or around 0.037%.