Question

The following table of data obtained from www.baseball-almanac.com shows hit information for four players. Suppose that one hit from the table is randomly selected.

Are "the hit being made by Hank Aaron" and "the hit being a double" independent events?

a. Yes, because P(hit by Hank Aaron | hit is a double) $=$P(hit by Hank Aaron)

b. No, because P(hit by Hank Aaron | hit is a double) $\ne$P(hit is a double)

c. No, because P(hit is by Hank Aaron | hit is a double) $\ne$P(hit by Hank Aaron)

d. Yes, because P(hit is by Hank Aaron | hit is a double) $=$P(hit is a double)

Short answer

The "hit being made by Hank Aaron" and the "hit being made by a double" are not independent events.

Step-by-step solution

Given information

Given the below data

Explanation

From the table, we get the following:

The probability that the hit is by Hank Aaron given that the hit is double is not equal to the probability hit by Hank Aaron.

P(hit is by Hank Aaron | hit is a double) = $\frac{624}{3771}\times \frac{1577}{12351}$

P(hit by Hank Aaron) =$\frac{3771}{12351}$

Therefore, they are not independent events as,

P(hit is by Hank Aaron | hit is a double) $\ne$P(hit by Hank Aaron)