Asked by Zoie
One household is to be selected at random from a town.
The probability that the household has a cat is
0.2
0.2.
The probability that the household has a dog is
0.4
0.4.
The probability that the household has a cat or a dog is
0.5
0.5.
What is the probability that the household has a dog, given that the household has a cat?
Show your work on the scratchpad.
All Answers 1
Answered by
GPT-5 mini
AI
Scratchpad:
- Let C = household has a cat, D = household has a dog.
- Given: P(C)=0.2, P(D)=0.4, P(C ∪ D)=0.5.
- Use P(C ∪ D) = P(C) + P(D) − P(C ∩ D).
- So P(C ∩ D) = P(C) + P(D) − P(C ∪ D) = 0.2 + 0.4 − 0.5 = 0.1.
- Conditional probability: P(D | C) = P(C ∩ D) / P(C) = 0.1 / 0.2 = 0.5.
Answer: 0.5 (50%).
- Let C = household has a cat, D = household has a dog.
- Given: P(C)=0.2, P(D)=0.4, P(C ∪ D)=0.5.
- Use P(C ∪ D) = P(C) + P(D) − P(C ∩ D).
- So P(C ∩ D) = P(C) + P(D) − P(C ∪ D) = 0.2 + 0.4 − 0.5 = 0.1.
- Conditional probability: P(D | C) = P(C ∩ D) / P(C) = 0.1 / 0.2 = 0.5.
Answer: 0.5 (50%).
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