Kerry's Improbable Medals

From: Tom Seim (soar2morrow_at_yahoo.com)
Date: 09/13/04 

Date: 12 Sep 2004 22:12:47 -0700

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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