Question

If A^c or `barA` or A' denote the complement of an event A, then P(A^c) = ______.

Answer 1

If A^c or `barA` or A' denote the complement of an event A, then P(A^c) = 1 – P(A).

Explanation:

Event A^c or 'not A' occurs if and only if event A does not occur.

Since A and A^c are mutually exclusive and exhaustive: 

\[P(A) + P\left(A^{c}\right) = 1\] 

\[\Rightarrow P\left(A^{c}\right) = 1 - P(A)\]