If the probability of simultaneous occurrence of two events A and B is p and the probability that exactly one of A, Boccurs is q, then which of the following is'are correct? 1. `P(bar(A)) +P(bar(B)) = 2 - 2p - q` . 2. `P(bar(A) nn bar(B))` = 1- p - q elect the correct answer using the code given below:

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

C

Explanation

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