Question

events (a) and (b) are mutually exclusive. (p(a) or (b)=p(a)+p(b)-p(a) and (b)) 8) (p(b)=\frac{9}{20}), (p(acup b)=\frac{3}{4}), (p(a)=?)

Explanation:

Step1: Recall the formula for mutually - exclusive events

For mutually exclusive events \(A\) and \(B\), \(P(A\cap B)=0\) and \(P(A\cup B)=P(A)+P(B)\).

Step2: Rearrange the formula to solve for \(P(A)\)

We know that \(P(A\cup B)=P(A)+P(B)\), so \(P(A)=P(A\cup B)-P(B)\).

Step3: Substitute the given values

Given \(P(B)=\frac{9}{20}\) and \(P(A\cup B)=\frac{3}{4}\). First, make the common denominator for \(\frac{3}{4}\), which is \(\frac{3\times5}{4\times5}=\frac{15}{20}\). Then \(P(A)=\frac{15}{20}-\frac{9}{20}\).

Step4: Calculate the result

\(P(A)=\frac{15 - 9}{20}=\frac{6}{20}=\frac{3}{10}\).

Answer:

\(\frac{3}{10}\)