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"?

Answer 1

Mathematically, two events are considered to be independent if the following relation holds true,

∵ P(B | A) = P(B)

For the given case,

P(D | L) = P(D)

But

0.13 ≠ 0.47

Since the relation doesn't hold true, therefore, "being left-handed" and "being a Democrat are not independent events.

Explanation:

We are given that

Left-handed = P(L) = 0.40

Democrats = P(D) = 0.47

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

P(D | L) = 0.13

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

Mathematically, two events are considered to be independent if the following relation holds true,

∵ P(B | A) = P(B)

For the given case,

P(D | L) = P(D)

But

0.13 ≠ 0.47

Since the relation doesn't hold true, therefore, "being left-handed" and "being a Democrat are not independent events.