Question

In a class, the probability that a randomly chosen student likes dogs is 0.72, that a student likes cats is 0.54, and that a student wants neither is 0.11. Find the probability that a student likes both dogs and cats

Answer 1

Let A be the event that a student likes a dog .

Let B be the event that a student likes a cat .

Then according to the problem, P(A) = 0.72 , P(B) = 0.54

A student wants neither means A^c B^c  

So P(A^c B^c) = P((A B)^c) = 1 - P(A B)

So P(A B) = 1 - P(A^c B^{​​​​​​c}) = 1 - 0.11 = 0.89

Probability that a student likes both dogs and cats

P(A B) = P(A) + P(B) - P(A B) = 0.72 + 0.54 - 0.89 = 0.37