Multiple Choice
About 15% of people in a town have both a cat and a dog. As 64% of residents have a dog, what is the probability that someone in the town owns a cat, given they have a dog?
4. Probability
Multiplication Rule: Dependent Events
Multiple Choice
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
Verified step by step guidance1
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 constant at 52 for both draws.
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 \( P(\text{First Ace}) = \frac{4}{52} \).
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 of drawing an ace on the second draw is \( P(\text{Second Ace}) = \frac{4}{52} \).
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 \( P(\text{Two Aces}) = P(\text{First Ace}) \times P(\text{Second Ace}) = \frac{4}{52} \times \frac{4}{52} \).
Step 5: Simplify the expression to find the final probability. The result will be a decimal value that matches one of the provided options.
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