Question

1. given event a, event b, and event c. event a and event b are mutually exclusive. event a and event c are not mutually exclusive.

p(a) = 0.45
p(b) = 0.35
p(c) = 0.25
what is the probability of the complement of event a?

1.00

0.55

0.10

0.45

Explanation:

Step1: Recall the complement rule

The complement rule in probability states that the probability of the complement of an event \( A \), denoted as \( P(A^c) \), is given by \( P(A^c)=1 - P(A) \).

Step2: Substitute the given value

We are given that \( P(A) = 0.45 \). Substituting this value into the complement rule formula, we get \( P(A^c)=1 - 0.45 \).

Step3: Calculate the result

Calculating \( 1 - 0.45 \), we obtain \( 0.55 \).

Answer:

0.55