2026 PCSS P1 Q8

A bag contains 10 red pens and 6 black pens.

Two pens are chosen from the bag at random without replacement.

Fred claims that the probability that one pen is a red pen and one pen is a black pen can be calculated using \(\left(\dfrac{10}{16}\right)\left(\dfrac6{15}\right)=\dfrac14\).

Explain why Fred’s claim is not true and find the actual probability.[2]