Li throws two fair four-sided dice, each numbered 1, 2, 3 and 4 - OCR - GCSE Maths - Question 4 - 2021 - Paper 1

The prime numbers from the unique scores are: 2, 3. Thus, the prime scores are 2 and 3.

There are a total of 4 (sides of the first die) × 4 (sides of the second die) = 16 total outcomes.

The outcomes yielding prime numbers (2 from (1,2) and (2,1), 3 from (1,3) and (3,1)) are:

1. (1,2)
2. (2,1)
3. (1,3)
4. (3,1)

Total outcomes resulting in prime scores = 4.

The probability P that Li's score is prime is given by:

$P = \frac{\text{Number of prime outcomes}}{\text{Total outcomes}} = \frac{4}{16} = \frac{1}{4}$