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Which equation shows that events A and B are independent?
AP(A and B) = P(A) + P(B) holds true
BP(A and B) = P(A)P(B) holds true
CP(A and B) = 0 holds true for them
DP(A or B) = P(A)P(B) holds true
Answer & Solution
Correct answer: B. P(A and B) = P(A)P(B) holds true
1. Independence means knowing that one event happened leaves the chance of the other unchanged.
2. That is captured by P(A and B) equal to P(A) times P(B).
3. A joint probability of zero is the test for mutually exclusive events, which is a different condition 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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