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?
4. Probability
Multiplication Rule: Dependent Events
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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?
A
0.23
B
0.15
C
0.64
D
0.096
Verified step by step guidance1
Step 1: Identify the given probabilities. The problem states that 15% of people have both a cat and a dog, which is the joint probability P(Cat ∩ Dog) = 0.15. Additionally, 64% of residents have a dog, so P(Dog) = 0.64.
Step 2: Recall the formula for conditional probability. The probability of owning a cat given that someone owns a dog is expressed as P(Cat | Dog) = P(Cat ∩ Dog) / P(Dog).
Step 3: Substitute the given values into the formula. Replace P(Cat ∩ Dog) with 0.15 and P(Dog) with 0.64 in the formula: P(Cat | Dog) = 0.15 / 0.64.
Step 4: Simplify the fraction to calculate the conditional probability. Perform the division to find the value of P(Cat | Dog).
Step 5: Interpret the result. The calculated value represents the probability that a person owns a cat, given that they already own a dog.
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