Question

Find the probability \( P\left(E^{C}\right) \) if \( P(E)=0.42 \). The probability \( P\left(E^{C}\right) \) is (Simplify your answer.)

Answer 1

The probability of the complement of event E, P(E^C), is 0.58.

Explanation:

The concept used to find the probability of the complement of an event is a fundamental concept in probability theory.

The complement of an event E, denoted as E^C, refers to all the outcomes that are not in E.

The probability of the complement of an event E, P(E^C), can be calculated using the formula:

P(E^C) = 1 - P(E)

This formula states that the probability of the complement is equal to one minus the probability of the event itself.

In the given question, the probability of event E is given as P(E) = 0.42.

To find the probability of the complement, we can substitute this value into the formula:

P(E^C) = 1 - 0.42

P(E^C) = 0.58

Therefore,

The probability of the complement of event E, P(E^C), is 0.58.