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 1

Answer:

option (B) is correct

Step-by-step explanation:

Concept:

Addition theorem of probability

P(A U B) = P(A) +P(B) - P(A∩B)

Conditional probability of A given B

P(A/B)= P(A∩B) / P(B)

Given:

P(A) +P(B) - P(A∩B) = P(A)

P(B) - P(A∩B) = 0

P(B) = P(A∩B)

P(A∩B) = P(B)

P(A∩B)/ P(B) = 1

P(A|B) = 1

Answer 2

Answer:

(B) is the answer

Step-by-step explanation:

Hi,

Given that P(A) + P(B) - P(A ∩ B ) = P(A)

On Cancelling out P(A) on both sides, we gt

⇒ P(B) = P(A ∩ B )

⇒P(A ∩ B ) / P(B) = 1------(1)

But, from the definition of condition probability,

we know that P(A/B) = P(A ∩ B )/P(B),

But from equation (1), we got P(A ∩ B )/P(B) = 1,

Hence, P(A/B) = 1

Hope, it helps !