Today's puzzler/probabilities - timely with financial crisis!

How timely the puzzler of 2 workers with less than 100% dependable cars needing to get to the farm job. not to nitpick, but the answer is ok so long as the failure probabilities are uncorrelated. that is to say, the cars don’t start coincidentally with heat/cold, rain or other common conditions.

Tappet bro’s, I purposefully posted this as your listeners that got the answer right can appreciate a similarity to why cdo’s and siv’s became “toxic”. Wanting for a more in depth explanation other than calling them “complex”, I stumbled upon the site below with a great explanation (I have no affiliation with it. in fact, don’t suggest any other page than the one listed is of interest. Originally I found it googling a story “nightline jeff greene subprime” and later “greenspan JOHN paulson wsj”).

I hope your educated listnership finds it as interesting as I did (and it took me over an hour to relocate the url)!

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A primer on financial engineering and structured finance

How financial engineers made a fortune creating worthless mortgage-based securities. (23-Jan-2008)

"What’s the probability that P will pay out \$1000? The probability of payout from each of X and Y is 95%, and we assume that those are INDEPENDENT probabilities.

So the probability that EITHER X or Y will pay out is 1-(1-.95)*(1-.95) = 1-0.0025 = .9975 = 99.75%.

So the probability that P will default is 0.25%, which gives it an A rating (which requires a default probability of 0.343% or lower).

The magic has started: I’ve taken two BB rated securities, and created from them an A rated security.

“What went wrong? Remember, a few paragraphs back, we said that the probability of payout from each of X and Y is 95%, and we assume that those are INDEPENDENT probabilities. Well, if X and Y are both related to subprime mortgages, then these probabilities are no longer independent, and so the computations come out wrong.”

http://www…cdo080123