which of the following best shows the relationship between the probability of an event, a, and its…

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

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

Answer

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