Concept explainers
True-false exam: A section of an exam contains four true-false questions. A completed exam is selected at random, and the four answers are recorded.
- List all 16 outcomes in the
sample space . - Assuming the outcomes to be equally find the
probability that all the answers are the same. - Assuming the outcomes to be equally find the probability that exactly one of the four answers is "True."
- Assuming the outcomes to be equally likely, find the probability that two of the answers are "True" and two of the answers are "false."
a.
To list all the outcomes of the sample space.
Answer to Problem 29E
Explanation of Solution
Given:
In an exam, there is a section that consists of 4 true/false questions.
Calculation:
The total questions are four and there are two choices for each question, which is true or false.
Therefore, total outcomes are
Let T represents true and F represents false.
The sample space is,
b.
To find the probability that all the answers are the same.
Answer to Problem 29E
The probability that all the answers are the same is
Explanation of Solution
Calculation:
From subpart (a), we have the sample space
Let
Therefore
Hence the probability that all the answers are the same is,
c.
To find the probability that exactly one of the four answers is true.
Answer to Problem 29E
The probability that exactly one of the four answers is true is
Explanation of Solution
Calculation:
From subpart (a), we have the sample space
Let
Therefore
Hence the probability that exactly one of the four answers is true is,
d.
To find the probability that two of the answers are true and two of the answers are false.
Answer to Problem 29E
The probability that two of the answers are true and two of the answers are false is
Explanation of Solution
Calculation:
From subpart (a), we have the sample space
Let
Therefore
Hence the probability that two of the answers are true and two of the answers are false is,
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Chapter 5 Solutions
Loose Leaf Version For Elementary Statistics
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