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brepped Paher s n a a mine CG The ist door leads to a after s kours d trael. The 2nd door that neturns him to the mine ofter tunnel that

brepped Paher s n a a mine CG The ist door leads to a after s kours d trael. The 2nd door that neturns him to the mine ofter tunnel that

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A miner is trapped in a mine containing 3 doors. The ist door londh to a tomnel that tohes hom to sofety after 5 Rours that neturns 'Rim to the mine after 4 hours. And the 3rd doarj leads to tunnelj that returas him to the mine dter I hour. of trovel. The 2nd door leads toa tunnel Assuming that the miner is of oll times equally likely to choose Cony ore door, what is the expected" long th time untilo the miner reaches sotoly? of of
Transcribed Image Text:A miner is trapped in a mine containing 3 doors. The ist door londh to a tomnel that tohes hom to sofety after 5 Rours that neturns 'Rim to the mine after 4 hours. And the 3rd doarj leads to tunnelj that returas him to the mine dter I hour. of trovel. The 2nd door leads toa tunnel Assuming that the miner is of oll times equally likely to choose Cony ore door, what is the expected" long th time untilo the miner reaches sotoly? of of
Expert Solution
Step 1

Let X be the length of time until the miner reaches safety and Y denotes the initial door number.

From the given information, there are 3 doors.

The 1st door leads to a tunnel that takes him to safety after 5 hours of travel.

That is, EX|Y=1=5

The 2nd door leads to a tunnel that takes him to mine after 4 hours.

That is, EX|Y=2=4+EX

The 3rd door leads to a tunnel that returns him to the mine after 1 hour.

That is, EX|Y=3=1+EX

Assuming that the miner is of all times equally likely to choose any of one door.

That is,

P(Y=1)=P(Y=2)=P(3)=1/3

 

 

 

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