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Felicity enrols in maths with probability 0.2, in speech with 0.65 and in both with 0.1625. What is the probability she enrols in maths or speech?
AThe probability is 0.8500
BThe probability is 0.7125
CThe probability is 0.6875
DThe probability is 0.4875
Answer & Solution
Correct answer: C. The probability is 0.6875
1. The addition rule is P(maths) plus P(speech) minus P(both).
2. The two separate probabilities add to 0.2 plus 0.65, which is 0.85.
3. The joint probability of both is 0.1625.
4. Subtracting gives 0.85 minus 0.1625, which is 0.6875.
5. Stopping at 0.8500 forgets the subtraction and double counts the students taking both.
6. The value 0.4875 subtracts the joint probability twice over.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.3 Two Basic Rules of Probability_
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