Question

With probability 0.6, the present was hidden by mom; with probability 0.4, it was hidden by dad. When mom hides the present, she hides it upstairs 70 percent of the time and downstairs 30 percent of the time. Dad is equally likely to hide it upstairs or downstairs. Given that it is downstairs, what is the probability it was hidden by dad?

Answer 1

Answer:-

Given that:-

Given that it is downstairs,

With probability 0.6, the present was hidden by mom; with probability 0.4, it was hidden by dad. When mom hides the present, she hides it upstairs 70 percent of the time and downstairs 30 percent of the time. Dad is equally likely to hide it upstairs or downstairs.

Let A denote event that  present was hidden by mom.

Let B denote event that  present was hidden by dad.

Let E denote event that she hides in upstairs.

Let F denote event that she hides in downstairs.

Given that

P(A) = 0.6

P(B)=0.4

P(E\A)=0.70

P(F\A)=0.30

P(E\B)=0.5

P(F\B)=0.5

what is the probability it was hidden by dad?

The probability that was hidden by dad if it is downstairs is