Question

Suppose that the handedness of the last fifteen U.S. presidents is as follows:

40% were left-handed (L)
47% were Democrats (D)

If a president is left-handed, there is a 13% chance that the president is a Democrat.

Based on this information on the last fifteen U.S. presidents, is "being left-handed" independent of "being a Democrat"?

(A) Yes, since 0.40 * 0.47 is not equal to 0.13.
(B) No, since 0.40 is not equal to 0.13.
(C) No, since 0.47 is not equal to 0.13.
(D) Yes, since 0.47 is not equal to 0.13.

Answer 1

Answer:

(C) No, since 0.47 is not equal to 0.13.

Step-by-step explanation:

We have two events, A and B.

I am going to say that P(A) is the probability that a president is left-handed.

I am going to say that P(B) is the probability that a president is a Democrat.

P(B/A) is the probability that the probability that the president is a Democrat, given that he is left-handed.

If P(B/A) = P(A), then the events are independent.

In this problem, we have that P(B/A) = 0.13 and P(A) = 0.47. So, "being left-handed" is not independent of "being a Democrat" and the correct answer is

(C) No, since 0.47 is not equal to 0.13.