Back to 3.3 Two Basic Rules of Probability

3.3 Exercise 38

Avg difficulty 2.5

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.

Name Single Double Triple Home Run Total Hits
Babe Ruth 1,517 506 136 714 2,873
Jackie Robinson 1,054 273 54 137 1,518
Ty Cobb 3,053 724 295 117 4,189
Hank Aaron 2,294 624 98 755 3,771
Total 7,918 2,127 583 1,723 12,351

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

  1. Yes, because P(hit by Hank Aaron|hit is a double) = P(hit by Hank Aaron)
  2. No, because P(hit by Hank Aaron|hit is a double) ≠ P(hit is a double)
  3. No, because P(hit is by Hank Aaron|hit is a double) ≠ P(hit by Hank Aaron)
  4. Yes, because P(hit is by Hank Aaron|hit is a double) = P(hit is a double)

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Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.