Two Basic Rules of Probability · Exercise 27

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.

$$\begin{array}{cccccc}\text{Name}& \text{Single}& \text{Double}& \text{Triple}& \text{Home Run}& \text{Total Hits}\\ \text{Babe Ruth}& \text{1,517}& \text{506}& \text{136}& \text{714}& \text{2,873}\\ \text{Jackie Robinson}& \text{1,054}& \text{273}& \text{54}& \text{137}& \text{1,518}\\ \text{Ty Cobb}& \text{3,053}& \text{724}& \text{295}& \text{117}& \text{4,189}\\ \text{Hank Aaron}& \text{2,294}& \text{624}& \text{98}& \text{755}& \text{3,771}\\ \text{Total}& \text{7,918}& \text{2,127}& \text{583}& \text{1,723}& \text{12,351}\end{array}$$
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) ≠ P(hit is a double)
(c) No, because P(hit is by Hank Aaron|hit is a double) ≠ P(hit by Hank Aaron)
(d) Yes, because P(hit is by Hank Aaron|hit is a double) = P(hit is a double)

OpenStax, Introductory Statistics 2e · §3.3 Two Basic Rules of Probability · Exercise 27