Probability of Ranger, Turfmaster & Colt Riding Mowers

[eyesclosed]

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?

 

[HallsofIvy]

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.

 

[eyesclosed]

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 ...

 

[HallsofIvy]

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?