Determine whether the events A and B are independent
A card is selected at random from a standard deck of 52 cards. It is then replaced and a second card is selected at random
Event A: a club is selected on the first draw
Event B: an ace is selected on the second draw
The events A and B are independent if the occurrence of one event does not affect the probability of the other event occurring.
In this case, event A is the selection of a club on the first draw, and event B is the selection of an ace on the second draw. The probability of selecting a club on the first draw is 13/52 because there are 13 clubs in a standard deck of 52 cards.
Since the card is replaced after the first draw, the probability of selecting an ace on the second draw is also 4/52 because there are 4 aces in a standard deck of 52 cards.
To determine if events A and B are independent, we will simply multiply the probabilities of each event occurring: (13/52) * (4/52) = 1/52.
Since the probability of both events occurring is equal to the product of their individual probabilities, we can conclude that events A and B are independent.