Two boxes, the first contains 3 red & 2 white balls. The second box contains 4 red & 7 white balls.
A fair die is tossed. If the outcome is even, a ball is drawn from the first box, while a ball is drawn from the second box if the outcome is odd.
Find the probability that a randomly chosen ball will be white and it comes from the first box.
Attempt at solution:
P(drawing from first box)= 3/6= 1/2, P(drawing a white ball)=9/16, P(White ball ∩ first box)= P(White ball | first box)xP(First box) =(2/5)(1/2)=1/5,
My friend says that the required probability is not P( White ball ∩ first box) but instead it's P(White ball | first box), which is it?