Sets 3

2 marks · Hard

Out of 80 participants in a charity run, 48 ran the full course, 35 took part in the half course, and 18 ran both the full and half course.

What is the probability that a randomly selected participant ran at least one of the two courses?

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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or 0.8125 or 13/16 (±0.0001)

Also accept: 13/16; 0.8125; 65/80

Common mistakes: Adding 48 + 35 instead of using inclusion-exclusion

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Marking points

M1 · 1 mark · Correct method to find total in at least one: n(F) + n(H) - n(F ∩ H)

A1 · 1 mark · Final probability as a simplified fraction, decimal, or percentage

Worked solution

Number who ran at least one = .

Probability = or or .