In a recent survey of local business owners, 40% of the respondents belong to the Rotary Club and 70% belong to the Chamber of Commerce.30% were members of both.Are the events "member of Chamber" and "member of Rotary" statistically independent?
A)Yes, since P(Chamber given Rotary) is equal to P(Rotary)
B)Yes, since P(Chamber given Rotary) is equal to P(Chamber)
C)Yes, since P(Rotary given Chamber) is equal to P(Chamber)
D)No, since P(Chamber given Rotary) is not equal to P(Rotary)
E)No, since P(Chamber given Rotary) is not equal to P(Chamber)

Question

Quizplus · Accepted Answer

Two events A and B are statistically independent if and only if P(A and B) = P(A) * P(B). Here, P(Chamber and Rotary) = 0.30, P(Chamber) = 0.70, and P(Rotary) = 0.40. If they were independent, P(Chamber and Rotary) should equal 0.70 * 0.40 = 0.28, but it's 0.30. Therefore, they are not independent, and the correct answer is that P(Chamber given Rotary) is not equal to P(Chamber), indicating dependence.

In a Recent Survey of Local Business Owners, 40% of the Respondents