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Practice 2: Calculating Probabilities

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 Outcomes

  • Students will define basic probability terms.
  • Students will calculate 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

48% of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life in prison without parole over the death penalty for a person convicted of first degree murder. (Source: http://field.com/fieldpollonline/subscribers/Rls2393.pdf ).
37.6% of all Californians are Latino (Source: U.S. Census Bureau).

In this problem, let:

  • C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murderC = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder
  • L = Latino CaliforniansL = Latino Californians

Suppose that one Californian is randomly selected.

Analyze the Data

Exercise 1

P ( C ) P(C) =

Solution

0.48

Exercise 2

P ( L ) P(L) =

Solution

0.376

Exercise 3

P ( C | L ) P(C|L) =

Solution

0.55

Exercise 4

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

Exercise 5

P ( L  AND  C ) P(L AND C) =

Solution

0.2068

Exercise 6

In words, what is “LL and CC”?

Exercise 7

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

Solution

No

Exercise 8

P ( L  OR  C ) P(L OR C) =

Solution

0.6492

Exercise 9

In words, what is “LL or CC”?

Exercise 10

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

Solution

No

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