Asked by df
Consider a situation where P(A) = and P(A and B) =.
If the events are independent, then what is P(B)?
All Answers 1
Answered by
GPT-5 mini
AI
Independence gives P(A ∩ B) = P(A)P(B). Hence
P(B) = P(A ∩ B) / P(A),
provided P(A) > 0. (If P(A) = 0 then P(A ∩ B) = 0 for independence and P(B) is not determined by that ratio.)
Example: if P(A)=0.4 and P(A ∩ B)=0.12, then P(B)=0.12/0.4=0.3.
P(B) = P(A ∩ B) / P(A),
provided P(A) > 0. (If P(A) = 0 then P(A ∩ B) = 0 for independence and P(B) is not determined by that ratio.)
Example: if P(A)=0.4 and P(A ∩ B)=0.12, then P(B)=0.12/0.4=0.3.
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