Question 33105
P(even,even)= P(even/even|A) + P(even/even|B)
P(even,even|A) = [P(EE and A)]/P(A) =[(4/9)(3/8)]/(1/2)= 1/3
P(even,even|B) = [P(EE and B)]/P(B) =[(2/5)(1/4)]/(1/2)= 1/5
So, P(EE) = 1/3 + 1/5 = 8/15
Comment:  I am not 100% confident this is the correct approach
but it is my best shot at it.
Cheers,
Stan H.