Question

If the probability of simultaneous occurrence of two events A and B is p and the probability that exactly one of A, B occurs is q, then which of the following is/are correct? 

1. P(bar A) + P(bar B) = 2 - 2p - q

2. P(bar A ∩ bar B) = 1 -  p - q

Select the correct answer using the code given below: 

a. 1 only 

b. 2 only 

c. Both 1 and 2 

d. Neither 1 nor 2

Answer 1

Correct option c. Both 1 and 2

Explanation:

P(A) + p(B) - 2P(A ∩ B) = q

P(A ∩ B) p

P(A) + P(B) = 2p +q

1 - p(bar A) + 1 - P(bar B) = p + q

P(bar A) + P(bar B) = 2 - 2p - q

P(bar A  ∩ bar B) = 1 - P(A ∪ B)

= 1 - (q + p) = 1 - p - q