Question

calculating the probability of independent events
two events, a and b, are independent. if ( p(a) = 0.3 ) and ( p(b) = 0.2 ), what is ( p(a \text{ and } b) )?

Explanation:

Step1: Recall the formula for independent events

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

Step2: Substitute the given values

Given \(P(A) = 0.3\) and \(P(B)=0.2\), then \(P(A\cap B)=0.3\times0.2\)

Step3: Calculate the product

\(0.3\times0.2 = 0.06\)

Answer:

\(0.06\)