
Concept explainers
a.
List the 23 possible outcomes in the
a.

Answer to Problem 26E
The 23 possible outcomes in the sample space are given as follows:
Explanation of Solution
Calculation:
The given information is that there are four copies of books that are left under the desk. The professor distributes to four students who lost their books.
Sample Space:
A sample space is the set of all possible outcomes of a random experiment.
There are four copies of books that are left under the desk. The first, second, third, and fourth numbers in the sample point represent the book that are received by students 1, 2, 3, and 4 respectively. For example, outcome
Therefore, 23 possible outcomes in the sample space are given as follows:
b.
List the outcomes in the
Compute the
b.

Answer to Problem 26E
The outcomes in the event ‘exactly two of the books are returned to their correct owners’ is
The probability of the event is
Explanation of Solution
Calculation:
The probability of any Event A is given below:
Event A denotes that exactly two students receive their own books.
Therefore, the outcomes those are in Event A are given as follows:
Among 24 outcomes in the sample space, 6 are in Event A. Substitute these values in the above equation.
The probability that exactly two students receive their own books is calculated as follows:
Thus, the probability that exactly two students receive their own books is
c.
Compute the probability that exactly one student receives his or her own book.
c.

Answer to Problem 26E
The probability that exactly one student receives his or her own book is
Explanation of Solution
Calculation:
It is given that there are four copies of the books that are left under the desk. The professor distributes randomly to four students who lost their books.
The probability of any Event A is given below:
From Exercise 34, it is clear that the sample space of the experiment is given below:
Event A denotes that exactly one student receives his or her own book. That is, either the first, second, third or fourth student receives his or her own book but exactly one of the four receives their own book.
Among 24 outcomes in the sample space, 8 are in Event A. Substitute these values in the above equation.
The probability that exactly one student receives his or her own book is calculated as follows:
Thus, the probability that exactly one student receives his or her own book is
d.
Find the probability that exactly three of the four students receive their own books.
d.

Answer to Problem 26E
The probability that exactly three of the four students receive their own books is 0.
Explanation of Solution
Calculation:
Event B denotes that exactly three students receive their own books.
If three of the students got their own books then automatically 4th student will also get her or his own book.
Hence, it is not possible that exactly three students receive their own books. Among 24 outcomes in the sample space, none of the outcomes are in Event B. Substitute these values in the above equation.
The probability that exactly three of the four students receive their own books is calculated as follows:
Thus, the probability that exactly three of the four students receive their own books is 0.
e.
Compute the probability that at least two students receive their own books.
e.

Answer to Problem 26E
The probability that at least two students receive their own books is
Explanation of Solution
Calculation:
The
If Events A, B, and C are three mutually exclusive events, then the addition rule is stated as follows:
The required probability is given below:
From Part (b), it is clear that the probability that exactly three students receive their own books is 0. There is only one possibility that all four receives their own books is
Therefore, the required probability is given below:
Thus, the probability that at least two students receive their own books is
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Chapter 6 Solutions
Introduction to Statistics and Data Analysis
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