Question

p(a)=0.27, p(b)=0.40, and p(a∩b)=0.670. are events a and b independent? justify the answer mathematically

Explanation:

Step1: Recall the formula for independent events

For two independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\)

Step2: Calculate \(P(A)\times P(B)\)

Given \(P(A) = 0.27\) and \(P(B)=0.40\), then \(P(A)\times P(B)=0.27\times0.40 = 0.108\)

Step3: Compare \(P(A\cap B)\) with \(P(A)\times P(B)\)

We have \(P(A\cap B)=0.670\) and \(P(A)\times P(B) = 0.108\). Since \(0.108
eq0.670\)

Answer:

No, because \((0.27)(0.40)
eq0.670\)