**Scenario: Agreement Probability on a Fabricated Story**Two students inform their professor that they missed an exam due to a car tire blowing out while driving into campus together. The professor, suspicious of the claim, separates the students and poses a straightforward question to each: "Which tire blew out?" Assuming the story is fabricated and the students did not coordinate their answers regarding the tire, what is the probability that they will both claim the same tire blew out?---**Analysis:**To solve this problem, we consider the possible outcomes for which tire it could be:1. Front Left2. Front Right3. Rear Left4. Rear RightIf each student randomly chooses a tire without prior coordination, there are four possible choices for each. The probability of both students choosing the same tire is calculated as follows:- Each student has a 1 in 4 chance of choosing any specific tire.- The probability that both independently choose the same tire (say, Front Left) is \( \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \). However, since they can accidentally agree on any of the four tires, the combined probability that they agree on any one of them is:\[ 4 \times \frac{1}{16} = \frac{1}{4} \]Thus, the probability that the students will both claim the same tire blew out is \( \frac{1}{4} \) or 25%.

Name: **Scenario: Agreement Probability on a Fabricated Story**Two students
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Description: **Scenario: Agreement Probability on a Fabricated Story**Two students inform their professor that they missed an exam due to a car tire blowing out while driving into campus together. The professor, suspicious of the claim, separates the students an

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Algebra

2. Two students tell their professor that they missed an exam because they were diving into campus together but a tire of their car blew out. The professor puts them in two separate rooms and asks each a simple question: Which tire blew out? Suppose the story is not true, and the students neglected to get their story straight in regard to which tire blew out. What is the probability that they will agree on which tire it was?

2. Two students tell their professor that they missed an exam because they were diving into campus together but a tire of their car blew out. The professor puts them in two separate rooms and asks each a simple question: Which tire blew out? Suppose the story is not true, and the students neglected to get their story straight in regard to which tire blew out. What is the probability that they will agree on which tire it was?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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