Re: Kerry's Improbable Medals

From: Fred Bloggs (nospam_at_nospam.com)
Date: 09/13/04 

Date: Mon, 13 Sep 2004 13:32:33 GMT

Okay- let's start with a more conventional warm-up before I grace your
post with an educated correction to all that REALLY sloppy thinking:

You have N letters and N envelopes pre-addressed to the N recipients of
the letters. What will be the probability of one or more letters going
to the correct recipient if you stuff the letters into the envelopes at
random (one per envelope of course)? Show derivations and compute result
for N=50.

Tom Seim wrote:
> A few days ago I posted a puzzler for Mr. Rocks for Brains. The
> puzzler was:
>
> 1. What is the probability that a Vietnam serviceman might earn a
> (any) medal?
>
> 2. What is the probability that a Vietnam serviceman might earn five
> medals?
>
> 3. What is the probability that a Vietnam serviceman might earn five
> medals consisting of 3 purple hearts, a bronze star and a silver star?
>
> Express the probability as its inverse, i.e. one in how many soldiers
> (the last question is best answered as one in how many Vietnam wars).
>
> Hint: these questions have a definite, calculable answer based on
> publically available data on the Internet.
>
> Of course, Mr. Rocks for Brains declined to answer, siting a pressing
> workload. Well, ok, perhaps pigs can fly too. Here is the answer:
>
> First, the total number of servicemen in Vietnam (1965-73): 2,594,000
>
> 1. Since there were 2,876,722 medals, of all types, awarded for the
> Vietnam War the probability of getting (any) a medal is 1.
>
> Narrowing it down, there were 220,516 Purple Hearts awarded (including
> Kerry's three), giving the probability of a (single) Purple Heart to
> be .085 (8.5%). There were 170,621 Bronze Stars awarded, giving a
> probability of .068 (6.8%0. And there were 21,630 Silver Stars
> awarded, yielding a probability of .00834 (0.834%).
>
> 2. If any medal is considered, the computed probability is still one
> (one to the fifth power). This, of course, is not realistic. A better
> way to think of it is that every serviceman got at least one medal,
> leaving only 282,722 medals available for a second, or subsequent,
> award. The probability of two awards is, then, .109 (10.9%). The
> probability of getting five medals of any type is, then, .000141
> (.0141%).
>
> 3. To compute Kerry's probability, lets look first at the probability
> of getting three purple hearts, which is .000614 (.0614%). Multiply
> this by the probabilities of getting a Bronze Star and a Silver Star
> and the combined grand total is:
>
> 3.37E-07 (.0000337%)
>
> Kerry, however, was only in theater for 132 days, while most everyone
> else was there for 365 days. This requires reducing the probability of
> each event by 132/365, or 0.362 (which is generous because 30 of those
> days were for training). While this doesn't seem like a lot, 0.362 to
> the fifth power is .00619. This results in the final answer of:
>
> 2.08E-09 (.00000000208%)
>
> Inverting this produces:
>
> 1 in 479,772,337
>
> As most of you know, you have much better odds of winning the Mega
> Lotto.
>
> Expressing this in terms of the number of Vietnam Wars we get:
>
> 185 Vietnam Wars
>
> In other words, we would expect the situation which produced the
> combination of events that produced Kerry's five medals only one in
> 185 VIETNAM WARS!
>
> So you think that there was no manipulation of the system to produce
> these medals? Go ahead, but the statistics are overwhelmingly against
> you.
>
> Tom

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