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Each of the 12 students in a class is given a fair

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 17E Chapter 1.4

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 17E

PROBLEM 17E

Each of the 12 students in a class is given a fair 12-sided die. In addition, each student is numbered from 1 to 12.

(a) If the students roll their dice, what is the probability that there is at least one “match” (e.g., student 4 rolls a 4)?

(b) If you are a member of this class, what is the probability that at least one of the other 11 students rolls the same number as you do?

Step-by-Step Solution:

Answer :

Step 1 of 2:

Each of 12 students in a class is given a fair 12-sided die. In addition,each student is numbered from 1 to 12.

a).

If the students roll their dice,we have to find the probability that there is at least one “match” .

Here A={at least one match} and

=none of them “match”

So P(A) = 1 - P()

P(at least one ‘match’) = 1-P(none of them “match”)

P(at least one ‘match’) = 1-

P(at least one ‘match’) = 1-

Step 2 of 2

Chapter 1.4, Problem 17E is Solved
Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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Each of the 12 students in a class is given a fair