Sets 3
3 marks · NormalLet and be sets in a universal set . Explain, using set notation, how to find the probability that an element chosen at random from lies in , and why you cannot simply add and unless and are disjoint.
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Common mistakes: Adding probabilities without considering the intersection
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Marking points
M1 · 1 mark · States or shows that the probability of is .
E1 · 1 mark · Explains why you subtract (to avoid double counting the overlap).
A1 · 1 mark · Comments that you can add and only if and are disjoint (so ).
Worked solution
The probability that a randomly chosen element is in is
This is because any element in both and would be counted twice if simply adding and . So, subtract to remove this double counting.
You can add only if , i.e., if the sets are disjoint and have no overlap.