Question

In his wardrobe, Timothy has 3 trousers. One of them is black, the second blue, and the third brown. In his wardrobe, he also has 4 shirts. One of them is black and the other 3 are white. He opens his wardrobe in the dark and picks out one shirt-trouser pair, without examining the colour. What is the likelihood that neither the shirt nor the trouser is black?

• A. 1/12
• B. 1/6
• C. 1/4
• D. 1/2

Answer 1

The Correct Option is D

Probability that trouser is not black =\(1-\frac{1}{3}=\frac{2}{3}\)
Probability that shirt is not black =\(1-\frac{1}{4}=\frac{2}{4}\)
Therefore, Required probability =\(\frac{2}{3}\times\frac{3}{4}=\frac{1}{2}\)
The correct answer is (D) :\(\frac{1}{2}\)