Archive for April, 2011

Let’s Make a Deal

April 21, 2011

I love this problem – even though it is just an exercise – it’s still kind of fun to work out.

It is also known as The Monty Hall and was floating around a while back in the early 1990’s on Marilyn vos Savant’s web page. Most of my current students have little or no idea who Monty Hall is and so I have fun explaining to them the whole idea behind the game show, Let’s Make a Deal.

Anyway, readers of this blog are probably familiar with the show and the problem, but for completeness sake, here it is in a nutshell.

You are on a game show where there are 3 doors. Behind two of the doors is a mule, and behind the third door is a Cadillac. You choose a door. The host then gives you an opportunity to switch your choice after opening one of the three doors – not the one you chose, of course – and revealing what is behind it. The question is, should you switch or keep to your original choice?

You have no doubt already clicked on the link above and checked out the solution, so you know that in the long run it is actually to your advantage to switch after the host reveals what is behind one of the unopened doors. But I have another question for you: What if there are 4 doors, and after you select one, the host reveals what is behind one of the remaining 3 doors – not the one you selected, of course – and gives you the option of switching. What should you do? And what is the exact probability of winning or losing in any case?

I’ll post an answer soon – unless you beat me to it! No Googling, now!

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Should I Repair or Rebuy?

April 19, 2011

I bought a top of the line front loading washer two years ago. It was on sale for $500.00. What a deal – the regular price was $899.00. Things were humming along nicely, laundry was getting done – until one morning I heard loud noises from the basement and ran down the steps to find the washer hopping across the floor. The load was out of balance, which is very bad for any type of washer, but most especially bad for a front loader.

The vibration was really severe and it resulted in some pretty serious damage to the drum – it came disconnected from the body of the washer, so it sort of hung there.

I called the repair guys. Since this is a foreign made washer (sorry all you “buy American” people – it was a good deal and the people I bought it from are Americans – also, the company that services it is American, so I guess I can rationalize it that way. . .). Worst case scenario was replace the drum for $387.00.

Got me thinking – what is my top line cut-off? How much before I say “I may as well just buy a new washer?”

So, I needed to know some things. Like, what is the yearly rate of depreciation for a washer?  How many years is a washer likely to last? Should I use the price I actually paid or the original price of $899.00 in figuring out the depreciation?

I, of course, went to Google and found this Depreciation Guide:

depreciation_cp-1-2

Apparently my washer has a useful lifetime of 8 years and depreciates by 12.5% per year. So, after two years what is it worth?

I’m just a little lazy today and would like you to figure this out for me. Should I buy new or repair?

By the way, the actual repair cost was a mere $167.00. Does this change your answer?