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Question
If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then ______.
Options
P (B|A) = 1
P (A|B) = 1
P (B|A) = 0
P (A|B) = 0
Solution
If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then P(A|B) = 1.
Explanation:
P(A) + P(B) – P(A ∩ B) = P(A)
⇒ P(B) − P(A ∩ B) = 0
P(A ∩ B) = P(B)
or `(P(A ∩ B))/(P(B))` = 1
P(A|B) = 1
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