Question

question 3 of 5 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? a and b are not 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. since p(a|b)=p(a) and p(b|a)=p(b), a and b are independent events.

Explanation:

Step1: Recall the condition for independent events

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

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

Given \(P(A) = 0.15\) and \(P(B)=0.34\), then \(P(A)\times P(B)=0.15\times0.34 = 0.051\). Since \(P(A\cap B)=0.051\), the events \(A\) and \(B\) are independent.

Answer:

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