Sets 3
3 marks · NormalA group of students was asked if they like music (M) and if they like art (A). Explain how you would use set notation and probability to work out the probability that a randomly selected student likes at least one of music or art, and the probability that a randomly selected student likes neither.
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Common mistakes: Confusing at least one with only one; Not using complements correctly
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Marking points
M1 · 1 mark · States (in formulas or words) that probability of 'at least one' is .
M2 · 1 mark · States that probability of 'neither' is .
A1 · 1 mark · Correct application of formulas, including referencing subtraction for the union: .
Worked solution
The probability that a randomly selected student likes at least one of music or art is:
The probability that a student likes neither is the complement: