Questions: Suppose a card is drawn at random from a standard deck. The card is then shuffied back into the deck. Then for a second time a card is drawn at random from the deck. The card is then shuffled back into the deck. Finally, for a third time a card is drawn at random from the deck. What is the probability of first drawing a red card, then a five, and then a black card? Do not round your intermediate computations. Round your final answer to four decimal places.

Solution Steps

There are 26 red cards (13 hearts and 13 diamonds) out of 52 total cards. So the probability of drawing a red card is 26/52 = 1/2.

There are four fives (one in each suit) out of 52 total cards. So the probability of drawing a five is 4/52 = 1/13.

There are 26 black cards (13 spades and 13 clubs) out of 52 total cards. So the probability of drawing a black card is 26/52 = 1/2.

Since the card is replaced after each draw, the events are independent. Therefore, the probability of all three events occurring is the product of their individual probabilities: (1/2) * (1/13) * (1/2) = 1/52.

Final Answer