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

Answer: (A)

Verified step by step guidance

1. 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.
2. 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).
3. 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.
4. Step 4: Simplify the fraction to calculate the conditional probability. Perform the division to find the value of P(Cat | Dog).
5. Step 5: Interpret the result. The calculated value represents the probability that a person owns a cat, given that they already own a dog.