Question

if ( p(a) = 0.36 ) and ( p(b) = 0.42 ) and ( a ) and ( b ) are independent, what is ( p(a \text{ or } b) )?

Explanation:

Step1: Recall the formula for \(P(A\ or\ B)\)

For independent events \(A\) and \(B\), \(P(A\ or\ B)=P(A)+P(B)-P(A)\times P(B)\)

Step2: Substitute the given values

Given \(P(A) = 0.36\) and \(P(B)=0.42\), substitute into the formula:
\(P(A\ or\ B)=0.36 + 0.42-0.36\times0.42\)

Step3: Calculate \(0.36\times0.42\)

\(0.36\times0.42 = 0.1512\)

Step4: Calculate \(0.36 + 0.42-0.1512\)

\(0.36+0.42 = 0.78\), then \(0.78-0.1512=0.6288\)

Answer:

\(0.6288\)