A box contains 6 black pens and 4 white pens. Two pens are taken out at random, one after the other, and the first pen is not put back before the second is taken. What is the probability that both pens are white?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{2}{15}\)
Without replacement, the first white pen stays out, so the second draw is made from one pen fewer and one white pen fewer. The probability of both draws is the product of the two probabilities.
Total pens \(=6+4=10\)
P(first pen white) \(\displaystyle =\frac{4}{10}=\frac{2}{5}\)
After that, 9 pens are left, of which 3 are white: P(second pen white) \(\displaystyle =\frac{3}{9}=\frac{1}{3}\)
P(both white) \(\displaystyle =\frac{2}{5}\times\frac{1}{3}=\frac{2}{15}\)