Question
What is the probability that a student has a dog given that they have a cat? Has a cat Does not have a cat Has a dog 3 17 Does not have a dog 4 6
Answers
GPT 3.5
To calculate the probability that a student has a dog given that they have a cat, we need to use the conditional probability formula:
P(A|B) = P(A and B) / P(B)
In this case, event A is having a dog and event B is having a cat. Given that a student has a cat, we know that there are 3 students who have both a cat and a dog, and a total of 3 + 4 = 7 students who have a cat. So:
P(A and B) = 3 (students with both a cat and a dog)
P(B) = 7 (students with a cat)
Therefore, the probability that a student has a dog given that they have a cat is:
P(A|B) = 3 / 7 ≈ 0.43 or 43%
P(A|B) = P(A and B) / P(B)
In this case, event A is having a dog and event B is having a cat. Given that a student has a cat, we know that there are 3 students who have both a cat and a dog, and a total of 3 + 4 = 7 students who have a cat. So:
P(A and B) = 3 (students with both a cat and a dog)
P(B) = 7 (students with a cat)
Therefore, the probability that a student has a dog given that they have a cat is:
P(A|B) = 3 / 7 ≈ 0.43 or 43%