Question

1. if the probability of rain is $\frac{3}{4}$, what is the probability it will not rain?

a. $\frac{1}{4}$
b. $\frac{3}{4}$
c. $\frac{1}{2}$
d. $\frac{3}{7}$

Explanation:

Step1: Recall the probability formula

The sum of the probability of an event \(A\) (rain) and its complement \(\overline{A}\) (not - rain) is \(P(A)+P(\overline{A}) = 1\).

Step2: Solve for \(P(\overline{A})\)

Given \(P(A)=\frac{3}{4}\), then \(P(\overline{A})=1 - P(A)\). Substitute \(P(A)\) into the formula: \(P(\overline{A})=1-\frac{3}{4}\).
Calculate \(1-\frac{3}{4}=\frac{4}{4}-\frac{3}{4}=\frac{4 - 3}{4}=\frac{1}{4}\).

Answer:

A. \(\frac{1}{4}\)