Question

let a and b be mutually exclusive events with ( p(a)=\frac{1}{4} ) and ( p(b)=\frac{1}{5} ). what is ( p(a \text{ or } b) )? write your answer as a fraction or decimal. do not round.

Explanation:

Step1: Recall the formula for mutually exclusive events

For mutually exclusive events \(A\) and \(B\), \(P(A\cup B)=P(A)+P(B)\).

Step2: Substitute the given probabilities

Given \(P(A)=\frac{1}{4}\) and \(P(B)=\frac{1}{5}\), then \(P(A\cup B)=\frac{1}{4}+\frac{1}{5}\).

Step3: Calculate the sum

Find a common denominator (20). \(\frac{1}{4}+\frac{1}{5}=\frac{1\times5}{4\times5}+\frac{1\times4}{5\times4}=\frac{5 + 4}{20}=\frac{9}{20}=0.45\).

Answer:

\(\frac{9}{20}\) or \(0.45\)