Question

question 4 of 8 select the correct answer. consider the probabilities shown below. p(a)=0.15 p(b)=0.34 p(a and b)=0.051 which of the following correctly justifies that a and b are independent events? since p(a|b)=p(b) and p(b|a)=p(a), a and b are independent events. since p(a|b)=p(b|a), a and b are independent events. a and b are not independent events. since p(a|b)=p(a) and p(b|a)=p(b), a and b are independent events.

Explanation:

Step1: Recall independence formula

For two independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\). Calculate \(P(A)\times P(B)\): \(0.15\times0.34 = 0.051\). Since \(P(A\cap B)=0.051\) and \(P(A\cap B)=P(A)\times P(B)\), events \(A\) and \(B\) are independent.

Answer:

Since \(P(A\cap B)=P(A)\times P(B)\), \(A\) and \(B\) are independent events.