Probability that box A is selected P(A)=21
Probability that box B is selected P(B)=21
Let E be the event that one ball is white while the other is red.
∴P(E)=P(A)⋅P(E/A)+P(B)⋅P(E/B)
=21[7C22⋅3+9C24⋅2]=21[216+368]=21[72+92]=6316
Thus, P(B/E)=P(E)P(B)P(E/B)=631691=167