A box has 5 black and 3 green shirts. One shirt is picked randomly and put in another box. The second box has 3 black and 5 green shirts. Now a shirt is picked from second box. What is the probability of it being a black shirt?

Answer: Option B

From box 1 we can pick black or green shirt
Case 1: Pick black shirt
Box 1 has total 5 + 3 = 8 shirts
Probability of black from box 1 = $$\frac{5}{8}$$
Now this black is added to box 2
So box 2 now has 3 + 1 = 4 black & 5 green shirts
Total = 4 + 5 = 9 shirts
Probability of black from box 2 = $$\frac{4}{9}$$
Case 1 probability
$$\begin{array}{rl}& =\frac{5}{8}\times \frac{4}{9}\\ & =\frac{20}{72}\end{array}$$

Case 2: Pick green shirt
Probability of green from box 1 = $$\frac{3}{8}$$
Now this green is added to box 2
So box 2 now has 3 black & 5 + 1 = 6 green shirts
Total = 3 + 6 = 9 shirts
Probability of black from box 2 = $$\frac{3}{9}$$
Case 2 probability
$$\begin{array}{rl}& =\frac{3}{8}\times \frac{3}{9}\\ & =\frac{9}{72}\end{array}$$
Total Probability
$$\begin{array}{rl}& =\frac{20}{72}+\frac{9}{72}\\ & =\frac{29}{72}\end{array}$$