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E and F are mutually exclusive with P(E) = 0.4 and P(F) = 0.5. What is P(E given F)?
AIt equals 0.40
BIt equals 0.80
CIt equals 0.00
DIt equals 0.20
Answer & Solution
Correct answer: C. It equals 0.00
1. Mutually exclusive means the joint probability of E and F is zero.
2. The conditional is the joint probability divided by P(F).
3. That gives 0 divided by 0.5, which is 0.00.
4. Put in words, once F has occurred E cannot occur at all.
5. Answering 0.40 would treat the events as independent, since it returns the plain probability of E.
6. Answering 0.80 divides 0.4 by 0.5 and uses the wrong numerator entirely.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.2 Independent and Mutually Exclusive Events_
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