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An event and its complement together cover the whole sample space and never overlap. What do their two probabilities do?
AThey add up to zero
BThey add up to two
CThey add up to one
DThey add up to half
Answer & Solution
Correct answer: C. They add up to one
1. The complement of a set contains all of the elements that are not in that set.
2. Every element of the sample space is therefore in either the event or its complement.
3. The union of the two covers the whole sample space with nothing left over.
4. Complementary events are also mutually exclusive, so nothing is counted twice.
5. The probability of observing an outcome from the sample space is 1.
6. Adding the two probabilities therefore gives exactly one, and anything larger would double count outcomes.
_Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 14: Probability_
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