Geoff has two fair spinners - OCR - GCSE Maths - Question 3 - 2018 - Paper 5

Geoff's error is in his calculation of the probability of the outcome being an even number or a prime number. Even numbers and prime numbers are not mutually exclusive; for example, 2 is both even and prime. This means that when he adds the probabilities, he double-counts the occurrence of 2.

To calculate the correct probability, we can use the principle of inclusion-exclusion:

Let:

• P(E) = Probability of an even outcome = 6/12
• P(P) = Probability of a prime outcome = 3/12
• P(E ∩ P) = Probability of being both even and prime = 1/12 (the outcome is 2)

The correct probability is: $ext{P(E or P)} = P(E) + P(P) - P(E ∩ P) = \frac{6}{12} + \frac{3}{12} - \frac{1}{12} = \frac{8}{12} = \frac{2}{3}$

Thus, the correct answer is ( \frac{8}{12} ) or simplified to ( \frac{2}{3} ).