Question

A box contains 42 blue and 22 black pens. A student wants to buy a blue pen. He picks up a pen at random and found it to be black. Holding the pen in his hand, he picks up another one at random without looking inside the box. What is the probability that the second pen is blue one?

• A. \(\frac{1}{3}\)
• B. \(\frac{2}{3}\)
• C. \(\frac{21}{32}\)
• D. \(\frac{5}{8}\)

Answer 1

The Correct Option is B

Total number of pens in the box = 42 blue + 22 black = 64 pens.
Since the first pen picked was black, the total number of pens left in the box is 63, and the number of blue pens remaining is 42.
Thus, the probability of picking a blue pen as the second pen is: \[ P(\text{Second pen is blue}) = \frac{\text{Number of blue pens left}}{\text{Total number of pens left}} = \frac{42}{63} = \frac{2}{3} \]

The correct option is (B): \(\frac{2}{3}\)