Probability of Ranger, Turfmaster & Colt Riding Mowers

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Homework Help Overview

The problem involves calculating the probabilities of different brands of riding mowers being brought in for warranty repairs based on their sales distribution and warranty claim rates. The subject area pertains to probability and statistics, specifically conditional probability.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the initial calculations provided by the original poster and question the validity of those calculations. Some suggest a more structured approach using hypothetical numbers to clarify the problem. There is an emphasis on justifying calculations and understanding the reasoning behind them.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's attempts and suggesting alternative methods for approaching the problem. There is no explicit consensus yet, as participants are exploring different interpretations and methods of calculation.

Contextual Notes

There is a noted lack of initial work shown by the original poster, which has led to requests for clarification on their understanding and approach. The discussion also highlights the importance of justifying calculations in probability problems.

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Perry’s Garden Center sells three brands of riding mowers—Ranger, Turfmaster, and Colt. Fifty percent of the riding mowers they sell are Rangers, thirty five percent Turfmasters, and fifteen percent Colts. Each brand of mower comes with a one-year parts and labor warranty. Based on their records, Perry knows that the chance of a warranty claim is five percent for the Ranger, 15% for the Turfmaster, and 25% for the Colt. If Perry’s service manager tells him that a riding mower has just been brought in for a repair covered by the warranty,
a. What is the chance that the riding mower is a Colt?
b. What is the chance that the riding mower is a Turfmaster?
c. What is the chance that the riding mower is a Ranger?
 
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You have posted a problem showing no work of your own. That makes it impossible to tell what you do know and where you have a problem. Please show what you have already tried on this so we will know what kind of help you need.
 
Here you go: a. 0.5*0.05 = 0.025 b. 0.15*0.35=0.0525 c. 0.25*0.15 =0.0375 !

But i am not sure if it is correct ...
 
Frankly, it looks like you are just putting numbers tohether at random. You should learn to justify each calculation you do (if nothing else, it would amaze your teacher!).

Here is what I would do. Imagine that there are 10000 mowers (to avoid percents and fractions). Then 50%, 5000 are Rangers, 35%, 3500, are Turfmasters, and 15%, 1500, are Colts.
5% of the Rangers, .05(5000)= 250, 15% of the Turfmasters, .15(3500)= 525, and .25% of the Colts, .25(1500)= 375, are brought in under warranty.
There are a total of 250+ 525+ 375= 1150 mowers brought in under warranty, 250 of them Rangers, 525 are Turfmasters, and 375 of them are Colts.

Now try to answer these questions:
Of all 1150 mowers brought in under warranty,

a. What is the chance that the riding mower is a Colt?
b. What is the chance that the riding mower is a Turfmaster?
c. What is the chance that the riding mower is a Ranger?
 

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