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?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
(1/52)^12 = ?
To find the probability of drawing 4 queens of hearts, 4 aces of spades, and 4 kings of clubs from 12 cards drawn with replacement, we need to determine the probability of drawing each card individually and then multiply those probabilities together.
Step 1: Determine the probability of drawing a queen of hearts.
Since there is only one queen of hearts in a standard deck of 52 cards, and we are drawing with replacement, the probability of drawing a queen of hearts in one draw is 1/52.
Step 2: Determine the probability of drawing an ace of spades.
Similar to the queen of hearts, there is only one ace of spades in a standard deck, so the probability of drawing an ace of spades is also 1/52.
Step 3: Determine the probability of drawing a king of clubs.
Again, there is only one king of clubs in a standard deck, so the probability of drawing a king of clubs is 1/52.
Step 4: Multiply the three probabilities together.
Since each draw is independent of the others, we can multiply the probabilities together to get the overall probability. Therefore, P(4 queens of hearts, 4 aces of spades, and 4 kings of clubs) = (1/52) * (1/52) * (1/52).
However, we need to draw 12 cards with replacement, so we need to repeat this process 12 times. Therefore, the overall probability of drawing 4 queens of hearts, 4 aces of spades, and 4 kings of clubs from 12 cards drawn with replacement is (1/52) * (1/52) * (1/52) raised to the power of 12.
Calculating this expression will give us the final probability.