Question

a and b are two events. given that ( p(a) = 0.25 ), ( p(b) = 0.3 ) and ( p(a \text{ and } b) = 0.05 ). drag and drop answers into the boxes to correctly complete the statement. events a and b are (square) because (square).

Explanation:

Step1: Calculate \(P(A|B)\)

By the formula \(P(A|B)=\frac{P(A\cap B)}{P(B)}\), substitute \(P(A\cap B) = 0.05\) and \(P(B)=0.3\). So \(P(A|B)=\frac{0.05}{0.3}=\frac{1}{6}\approx0.17\).

Step2: Compare \(P(A|B)\) with \(P(A)\)

Given \(P(A) = 0.25\). Since \(\frac{1}{6}\approx0.17
eq0.25\).

Answer:

Events \(A\) and \(B\) are not independent because \(P(A|B)
eq P(A)\)