Let A represent cat ownership and B represent dog ownership. Suppose 35% of households in a population own cats, 30% own dogs, and 15% own both a cat and a dog. Suppose you know that a household owns a cat. What is the probability that it also owns a dog?
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To find the probability that a household owns both a cat and a dog given that they own a cat, we can use the formula for conditional probability:
P(B | A) = P(A and B) / P(A)
First, let's calculate the probability of a household owning both a cat and a dog:
P(A and B) = 0.15
Next, let's calculate the probability of a household owning a cat:
P(A) = 0.35
Now we can plug these values into the formula:
P(B | A) = 0.15 / 0.35 ≈ 0.4286
Therefore, the probability that a household owns a dog given that they own a cat is approximately 0.43 or 43%.
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