There are only 3 red counters and 5 yellow counters in a bag - Edexcel - GCSE Maths - Question 17 - 2021 - Paper 1

To have exactly one red counter, Jude must choose 1 red counter from 3 and 2 yellow counters from 5. The number of ways to choose 1 red counter is:

inom{3}{1} = 3

The number of ways to choose 2 yellow counters is:

inom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10.

Thus, the total number of favorable outcomes is:

$$3 \times 10 = 30.$$

The probability of Jude taking exactly one red counter is the ratio of the number of favorable outcomes to the total number of ways to choose 3 counters:

$$P(\text{exactly 1 red}) = \frac{30}{56} = \frac{15}{28} \approx 0.536.$$