Box A: 2 white, 3 red, 2 black. Box B: 4 white, 2 red, 3 black. Two balls drawn without replacement from a randomly selected box; one turns out white, one red. Find the probability both came from box B.
Solutions · 1
Official solution
\[P(\text{W,R from B}) = \frac{{}^4C_1{}^2C_1}{{}^9C_2}=\frac29,\qquad P(\text{W,R from A}) = \frac{{}^2C_1{}^3C_1}{{}^7C_2}=\frac27\]
\[P(B\mid\text{event}) = \frac{2/9}{2/9+2/7} = \frac{14}{18+14}\ \cdots = \frac{7}{16}\]