12 cards are drawn with replacement from an ordinary deck of 52 cards. What is the probability that 4 queens of hearts, 4 aces of spades, and 4 kings of clubs are drawn?
since each card has a 1/52 chance of being drawn, that would be
(1/52)^12
To find the probability of drawing 4 queens of hearts, 4 aces of spades, and 4 kings of clubs in 12 cards drawn with replacement from a deck of 52 cards, we need to determine the probability of each individual event and then multiply them together.
Let's start with the probability of drawing a queen of hearts. There is only one queen of hearts in a deck of 52 cards, so the probability of drawing a queen of hearts on the first draw is 1/52. Since we are drawing with replacement, the probability will remain the same for each subsequent draw. Therefore, the probability of drawing 4 queens of hearts in 12 draws is (1/52)^4.
Similarly, the probability of drawing an ace of spades is 1/52, and the probability of drawing a king of clubs is also 1/52. So, the probability of drawing 4 aces of spades and 4 kings of clubs in 12 draws each would be (1/52)^4.
Finally, since we are drawing independent events, we can multiply these probabilities together to find the overall probability:
Probability = (1/52)^4 * (1/52)^4 * (1/52)^4 = (1/52)^(4+4+4) = (1/52)^12
Therefore, the probability of drawing 4 queens of hearts, 4 aces of spades, and 4 kings of clubs in 12 draws with replacement from a deck of 52 cards is (1/52)^12.