**Engine Failure Rates and Probability Calculation**In an article published in 2012 at Telegraph.co.uk, Warranty Direct provided engine failure rates for various car brands based on their database of UK direct consumer warranties. The known failure rates are listed below:- Hondas failed at a rate of 1 in 344.- Fords failed at a rate of 1 in 80.- Audis failed at a rate of 1 in 27.Suppose at a particular dealer:- Hondas account for 20% of sales,- Audis account for 30% of sales, and- Fords account for 50% of sales.Assuming the engine failure rates apply to these vehicles, we are to determine the probability that a randomly selected vehicle from this dealer will experience engine failure.To solve this, we use the law of total probability. The formula is:\[ P(\text{Engine Failure}) = P(\text{Engine Failure | Honda}) \times P(\text{Honda}) + P(\text{Engine Failure | Audi}) \times P(\text{Audi}) + P(\text{Engine Failure | Ford}) \times P(\text{Ford}) \]Given:- \( P(\text{Engine Failure | Honda}) = \frac{1}{344} \)- \( P(\text{Engine Failure | Audi}) = \frac{1}{27} \)- \( P(\text{Engine Failure | Ford}) = \frac{1}{80} \)And,- \( P(\text{Honda}) = 0.20 \)- \( P(\text{Audi}) = 0.30 \)- \( P(\text{Ford}) = 0.50 \)Substituting these values into the formula:\[ P(\text{Engine Failure}) = \left(\frac{1}{344}\right) \times 0.20 + \left(\frac{1}{27}\right) \times 0.30 + \left(\frac{1}{80}\right) \times 0.50 \]Calculate each term:\[ \frac{1}{344} \times 0.20 = 0.0005814 \]\[ \frac{1}{27} \times 0.30 = 0.0111111 \]\[ \frac{1}{80} \times 0.50 = 0.00625 \]

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Answered: In an article published in 2012 at…

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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