Question

if the p(a) =.3, p(b) =.65, and events a & b are independent, find the p(a 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 \(P(A) = 0.3\), \(P(B)=0.65\). Then \(P(A)\times P(B)=0.3\times0.65 = 0.195\)
And \(P(A)+P(B)=0.3 + 0.65=0.95\)

Step3: Calculate \(P(A\ or\ B)\)

\(P(A\ or\ B)=0.95- 0.195=0.755\)

Answer:

\(0.755\)