Question

If A and B are two independent events, then the probability of occurrence of at least one of A and B is given by,

(a) 1+ P(A′) P (B′)

(b) 1− P(A′). P (B′)

(c) 1− P(A′) + P (B′)

(d) 1− P(A′) – P (B′)

Answer 1

Answer : b) 1− P(A′). P (B′)

Explanation :

As the condition is given by occurrence of probability at least one of A and B. 

Therefore, the event is given by

P(A or B) = P(A ∪ B)

                 = P(A) + P(B) − P(A ∩ B)

                 = P(A) + P(B) − P(A) P(B)

                 = P(A) + P(B) [1−P(A)]

                 = P(A) + P(B). P(A′)

                 = 1− P(A′) + P(B) P(A′)

                 = 1− P(A′) [1− P(B)]

                 = 1− P(A′) .P (B′)

The formula used :

1. P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
2. P(A ∩ B) = P(A). P(B)
3. P(A') =1 - P(A) or P(A) = 1 - P(A')

(b) 1 - P(A') .P (B')