What is the probability of drawing four aces from a deck if the card is replaced each time?

To determine the correct answer, it is essential to understand the process of drawing cards from a deck with replacement and the principles of probability involved.

When drawing a card from a standard deck of 52 playing cards, the probability of drawing an ace during a single draw is 4 out of 52, or 1/13, since there are four aces in the deck. The important detail in this scenario is that the card is replaced after each draw. This means that the composition of the deck remains the same for each draw, ensuring that the probability of drawing an ace remains constant at 1/13 for each of the four draws.

Because these draws are independent events, the overall probability of drawing four aces in succession—where each draw maintains the probability of 1/13—is found by multiplying the probability of drawing an ace for each of the four draws together. This calculation can be expressed as (1/13) * (1/13) * (1/13) * (1/13), which simplifies to (1/13)^4.

Therefore, the probability of successfully drawing four aces in four attempts, with replacement of the card each time, is accurately represented by (1/13)^4.