alleryStart learning →When finding the probability that E or F occurs, why is the probability of E and F subtracted?
AThe shared outcomes are counted twice
BThe shared outcomes cannot ever occur
CThe two events must be made disjoint
DThe total probability must exceed one
Answer & Solution
Correct answer: A. The shared outcomes are counted twice
1. Adding the probability of E to the probability of E includes every outcome in each one.
2. Outcomes lying in both events appear in each of those two totals, so they are counted twice over.
3. Subtracting the probability of the intersection removes the duplicate count exactly once.
4. When the events share no outcomes there is nothing to subtract, so the formula reduces to a plain sum.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.7 Probability_
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