Question 360608
Let b1 = event that 1st ball drawn is black,
w1 = event that 1st ball drawn is white,
b2 = event that 2nd ball drawn is black,
w2 = event that 2nd ball drawn is white.
Then P(b1|w2) = P(b1 and w2)/P(w2)= P(b1 and w2)/[P(b1 and w2)+P(w1 and w2)]
=P(w2|b1)*P(b1)/[P(w2|b1)*P(b1) + P(w2|w1)*P(w1)]
={{{(3/10)*(4/7)/((3/10)*(4/7)+(2/5)*(3/7))}}}
={{{(12/70)/(12/70+6/35) = 1/2}}}