Question

In a card game, three cards are drawn from a deck with replacement. What is the probability of getting exactly two aces?

Answer 1

To find the probability of getting exactly two aces when three cards are drawn from a deck with replacement, we need to consider the number of ways this can occur. There are three possible scenarios, and by calculating the probabilities for each scenario, we can determine the overall probability.

Step-by-step explanation:

To find the probability of getting exactly two aces when three cards are drawn from a deck with replacement, we need to consider the number of ways this can occur. There are four aces in a deck of 52 cards, so the probability of drawing an ace on any single draw is 4/52 or 1/13.

When drawing three cards, there are three possible scenarios:

1. Getting two aces and one card that is not an ace. The probability of this is (1/13) * (1/13) * (12/13).
2. Getting one ace and two cards that are not aces. The probability of this is (1/13) * (12/13) * (12/13).
3. Getting no aces. The probability of this is (12/13) * (12/13) * (12/13).

Therefore, the probability of getting exactly two aces is the sum of the probabilities from scenarios 1 and 2: (1/13) * (1/13) * (12/13) + (1/13) * (12/13) * (12/13).