What is the probability that a card player draws two aces from a standard deck of 52 cards if they keep the first card after drawing it?

• A. 0.0035
• B. 0.0059
• C. 0.0045
• D. 0.0044

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the problem. A standard deck of cards has 52 cards, and there are 4 aces in the deck. The player draws two cards sequentially, keeping the first card after drawing it. This means the total number of cards remains 52 for both draws.
2. Step 2: Calculate the probability of drawing an ace on the first draw. Since there are 4 aces in the deck, the probability is given by \( P(\text{First Ace}) = \frac{4}{52} \).
3. Step 3: Calculate the probability of drawing an ace on the second draw. Since the first card is kept, the total number of cards remains 52, and there are still 4 aces in the deck. Thus, the probability is \( P(\text{Second Ace}) = \frac{4}{52} \).
4. Step 4: Multiply the probabilities of the two independent events (drawing an ace on the first draw and drawing an ace on the second draw). The combined probability is \( P(\text{Two Aces}) = P(\text{First Ace}) \times P(\text{Second Ace}) = \frac{4}{52} \times \frac{4}{52} \).
5. Step 5: Simplify the expression \( \frac{4}{52} \times \frac{4}{52} \) to find the final probability. This will give you the probability of drawing two aces under the given conditions.