A box contains 25 discs: The discs are either blue or yellow in the ratio 4 : 1 - OCR - GCSE Maths - Question 20 - 2023 - Paper 5

The total number of ways to choose 2 discs from 25 is given by the combination formula:

$C(n, k) = \frac{n!}{k!(n-k)!}$

Thus:

$C(25, 2) = \frac{25!}{2!(25-2)!} = \frac{25 \times 24}{2} = 300$

The number of ways to choose one blue and one yellow can be calculated as:

Number of ways to choose 1 blue = 20 Number of ways to choose 1 yellow = 5

Thus, the total ways to choose one blue and one yellow is:

$20 \times 5 = 100$

Now, we can find the probability that the two discs chosen are of different colours:

$P(different) = \frac{\text{Number of ways to pick one blue and one yellow}}{\text{Total ways to pick any two discs}}$

Substituting in the values:

$P(different) = \frac{100}{300} = \frac{1}{3}$