Question 369966
(a) P(red) = P(red AND b1) + P(red AND b2) + P(red AND b3)
=P(red|b1)*P(b1) + P(red|b2)*P(b2)+P(red|b3)*P(b3)
={{{(3/8)*(1/3) + (2/6)*(1/3) + (4/6)*(1/3) = 11/24}}}, assuming each box is equally likely to be chosen.
(b)  P(red|~b3) = {{{(3/8)*(1/2)+(2/6)*(1/2) = 17/48}}}