Question

You are told that P(A | B) = P(B | A). Which statement below must be true?



A) A and B are equally likely

B) P(A | B) = 0.5

C) A and B are independent

D) A and B are dependent

Answer 1

@perl

Answer 2

given P( A | B ) = P ( B | A )

this implies, by substituting

P ( A & B ) / P(B) = P( B & A ) / P (A)

Answer 3

Using the definition :
P ( X | Y ) = P( X & Y ) / P ( Y )

Answer 4

@AshleyLashae can you try to solve it now ? hint, cross multiply

Answer 5

A

Answer 6

and there is a commutativity rule you can apply as well:
P( A & B) = P( B & A )