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

If P (A|B) > P (A), then which of the following is correct:

A. P (B|A) < P (B)

B. P (A ∩ B) < P (A) . P (B)

C. P (B|A) > P (B)

D. P (B|A) = P (B)

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then

A. A ⊂ B

B. B ⊂ A

C. B = φ

D. A = φ

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known:

P (A fails) = 0.2

P (B fails alone) = 0.15

P (A and B fail) = 0.15

Evaluate the following probabilities:

(i) P (A fails | B has failed)

(ii) P (A fails alone)