Question

which of the following best shows the relationship between the probability of an event, a, and its complement, a^c?
a. p(a) < p(a^c)
b. p(a) = p(a^c)
c. p(a) = 1 - p(a^c)
d. p(a) > p(a^c)

Explanation:

Step1: Recall probability - complement rule

The sum of the probability of an event and its complement is 1. That is, $P(A)+P(A^{C}) = 1$.

Step2: Rearrange the formula

By subtracting $P(A^{C})$ from both sides of the equation $P(A)+P(A^{C}) = 1$, we get $P(A)=1 - P(A^{C})$.

Answer:

C. $P(A)=1 - P(A^{C})$