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"? Yes, since 0.40 * 0.47 is not equal to 0.13. Yes, since 0.47 is not equal to 0.13. No, since 0.47 is not equal to 0.13. No, since 0.40 is not equal to 0.13.

Correct option is: No, since 0.47 is not equal to 0.13.

Step-by-step explanation:

Independent events are those events that are not affected by the occurrence of other events.

If events A and B are independent then, P (A ∩ B) = P (A) × P (B).

Then the conditional probability of B when A has already occurred is:

It is provided that:

P (L) = 0.40

P (D) = 0.47

P (D|L) = 0.13.

If events D and L are independent then: P (D|L) = P (D).

But P (D|L) = 0.13 ≠ P (D) = 0.47.

Thus, the event of "being left-handed" is not independent of the event of being a Democrat.

The correct option is: No, since 0.47 is not equal to 0.13.

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