Asked by c
answer in the most simplest way and like a teen
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:
- P(cat) = 0.2
- P(dog) = 0.4
- P(cat or dog) = 0.5
- Use formula: P(cat or dog) = P(cat) + P(dog) - P(cat and dog)
- So P(cat and dog) = 0.2 + 0.4 - 0.5 = 0.1
- Conditional prob: P(dog | cat) = P(cat and dog) / P(cat) = 0.1 / 0.2 = 0.5
Answer:
The probability the household has a dog given it has a cat is 0.5 (50%).
- P(cat) = 0.2
- P(dog) = 0.4
- P(cat or dog) = 0.5
- Use formula: P(cat or dog) = P(cat) + P(dog) - P(cat and dog)
- So P(cat and dog) = 0.2 + 0.4 - 0.5 = 0.1
- Conditional prob: P(dog | cat) = P(cat and dog) / P(cat) = 0.1 / 0.2 = 0.5
Answer:
The probability the household has a dog given it has a cat is 0.5 (50%).
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