Question

the probability that an event will not happen is ( p(e)=\frac{1}{4} ). find the probability that the event will happen. the probability that the event will happen is ( square ). (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the probability formula

The formula for the probability of an event \(E\) and its complement \(E'\) is \(P(E)+P(E') = 1\).

Step2: Solve for \(P(E)\)

We know \(P(E')=\frac{1}{4}\). Substitute into the formula: \(P(E)=1 - P(E')\).
So \(P(E)=1-\frac{1}{4}\).
Calculate \(1-\frac{1}{4}=\frac{4}{4}-\frac{1}{4}=\frac{4 - 1}{4}=\frac{3}{4}\).

Answer:

\(\frac{3}{4}\)