SOLUTION: There are three brands of riding mowers: Ranger, Turfmaster, and Colt. Fifity percent of the riding mowers sold by a company are rangers, thirty five percent are turfmasters, and f

Question 469386: There are three brands of riding mowers: Ranger, Turfmaster, and Colt. Fifity percent of the riding mowers sold by a company are rangers, thirty five percent are 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 5% for the Ranger, 15% for the Turfmaster, and 25% for the Colt. If the company's manager tells a guy that a riding mower has just been brought in for a repair covered by the warranty, then
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?
What confuses me are the two different percentages..how do I use the information?Also, yes there is a similar question to this posted on the website but no one has answered it yet so I posted this again. Thank you for your help.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
There are three brands of riding mowers: Ranger, Turfmaster, and Colt.
Fifty percent of the riding mowers sold by a company are rangers,
thirty five percent are 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 5% for the Ranger, 15% for the Turfmaster, and 25% for the Colt.
-----------------------------------
If the company's manager tells a guy that a riding mower has just been brought in for a repair covered by the warranty, then
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?
What confuses me are the two different percentages..how do I use the information?
----
This is a Bayes Theorem problem. You probably have an example in
your text.
The 1st percentages are the percentage you have a Colt or a Turfmaster or
a Ranges mower.
---
The 2nd percentages are conditional percents that you need repair given
that you have a Colt, or you need repair given that you have a Turfmaster,
etc.
---
But P(Colt)*P(needs repair|Colt) = P(Colt AND needs repair)
---
With that info for each of the mowers you can figure out
probability you have a Colt or Turfmaster or Ranger.
=======================================================
Check your text for an example or check Bayes Theorem online.
=======================================================
Cheers,
Stan H.
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