If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are picture cards.
There are a total of 52 cards in a deck, and of those, there are 12 picture cards (King, Queen, and Jack) in each suit. Since there are four suits, there are a total of 12 x 4 = 48 picture cards in the deck.
To find the probability of drawing 4 picture cards, we need to find the probability of drawing a picture card for each of the 4 cards. Since each draw is independent, we can multiply the probabilities together to find the overall probability.
For the first card, the probability of drawing a picture card is 48/52, since there are 48 picture cards out of a total of 52 cards.
For the second card, after one picture card has been drawn, there are now 47 picture cards remaining out of a total of 51 cards. Therefore, the probability of drawing a picture card for the second card is 47/51.
For the third card, after two picture cards have been drawn, there are now 46 picture cards remaining out of a total of 50 cards. Therefore, the probability of drawing a picture card for the third card is 46/50.
For the fourth card, after three picture cards have been drawn, there are now 45 picture cards remaining out of a total of 49 cards. Therefore, the probability of drawing a picture card for the fourth card is 45/49.
To find the overall probability, we multiply these probabilities together:
(48/52) * (47/51) * (46/50) * (45/49) ≈ 0.2203
Therefore, the probability of drawing all 4 cards as picture cards is approximately 0.2203, or 22.03%.