Question:
If A and B are any two events such that P(A) + P(B) - P(A and B) = P(A), then (A) P(B|A) = 1 (B) P(A|B) = 1 (C) P(B|A) = 0 (D) P(A|B) = 0
Answer:
Given that P(A) + P(B) - P(A and B) = P(A)
=> P(A) + P(B) - P(A ∩ B) = P(A)
=> P(A) + P(B) - P(A ∩ B) - P(A) = 0
=> P(B) - P(A ∩ B) = 0
=> P(B) = P(A ∩ B)
Now
P(A/B) = P(A ∩ B)/P(B)
= P(B)/P(B)
= 1
=> P(A/B) = 1
So option B is the correct answer.
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