The star quarterback of a university football team has decided to return for one more season. He tells one person, who in turn tells someone else, and so on, with each person talking to someone who has not heard the news. At each step in this chain, if the message heard is "yes" (he is returning) then there is a 5% chance it will be changed to "no," and if the message heard is "no," then there is a 15% chance that it will be changed to "yes." Determine the probability that the fourth person in the chain hears the correct news. (A graphing calculator is recommended. Assume that the quarterback is not part of the chain. Round your answer to one decimal place.)
The star quarterback of a university football team has decided to return for one more season. He tells one person, who in turn tells someone else, and so on, with each person talking to someone who has not heard the news. At each step in this chain, if the message heard is "yes" (he is returning) then there is a 5% chance it will be changed to "no," and if the message heard is "no," then there is a 15% chance that it will be changed to "yes." Determine the probability that the fourth person in the chain hears the correct news. (A graphing calculator is recommended. Assume that the quarterback is not part of the chain. Round your answer to one decimal place.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![The star quarterback of a university football team has decided to return for one more season. He tells one person, who in turn tells someone else, and so on, with each person talking to someone who has not
heard the news. At each step in this chain, if the message heard is "yes" (he is returning) then there is a 5% chance it will be changed to "no," and if the message heard is "no," then there is a 15% chance that it
will be changed to "yes." Determine the probability that the fourth person in the chain hears the correct news. (A graphing calculator is recommended. Assume that the quarterback is not part of the chain. Round
your answer to one decimal place.)
%](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F532cb823-0c19-4b15-a905-a7d232958517%2F2c29ddf3-d8b6-4067-947e-baba04881172%2F09a6pv7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The star quarterback of a university football team has decided to return for one more season. He tells one person, who in turn tells someone else, and so on, with each person talking to someone who has not
heard the news. At each step in this chain, if the message heard is "yes" (he is returning) then there is a 5% chance it will be changed to "no," and if the message heard is "no," then there is a 15% chance that it
will be changed to "yes." Determine the probability that the fourth person in the chain hears the correct news. (A graphing calculator is recommended. Assume that the quarterback is not part of the chain. Round
your answer to one decimal place.)
%
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Given that:
If the message heard is Yes then there is a 5% chance it will be changed to no so the remaining 95% is yes.
If the message heard is No then there is a 15% chance it will be changed to Yes so the remaining 85% is no.
To get the probability we need to find the by using the Markov matrix.
M represents and x represents .
Multiple M by x and repeat this process till .
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