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Probability Topics: Practice II

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module allows students to practice using what they've learned about Probability. Students will apply their understanding of basic probability terms, calculate probabilities based on the data provided, and determine whether events are independent or mutually exclusive.

Student Learning Objectives

  • Students will define basic probability terms.
  • Students will practice calculating probabilities.
  • Students will determine whether two events are mutually exclusive or whether two events are independent.

Note:

Use probability rules to solve the problems below. Show your work.

Given

68% of Californians support the death penalty. A majority of all racial groups in California support the death penalty, except for black Californians, of whom 45% support the death penalty (Source: San Jose Mercury News, 12/2005). 6% of all Californians are black (Source: U.S. Census Bureau).

In this problem, let:

  • CC = Californians supporting the death penalty
  • BB = Black Californians

Suppose that one Californian is randomly selected.

Analyze the Data

Exercise 1

P ( C ) P(C) =

Solution

0.68

Exercise 2

P ( B ) P(B) =

Solution

0.06

Exercise 3

P ( C | B ) P(C|B) =

Solution

0.45

Exercise 4

In words, what is " C | B C | B "?

Exercise 5

P ( B  AND  C ) P(B AND C) =

Solution

0.027

Exercise 6

In words, what is “BB and CC”?

Exercise 7

Are BB and CC independent events? Show why or why not.

Solution

No

Exercise 8

P ( B  OR  C ) P(B OR C) =

Solution

0.713

Exercise 9

In words, what is “BB or CC”?

Exercise 10

Are BB and CC mutually exclusive events? Show why or why not.

Solution

No

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