Mysterious JFK witness deaths: A probability analysis

This analysis calculates the probability of at least 15 witnesses dying UNNATURAL deaths within one year of the JFK assassination. The deaths were a combination of homicides, suicides, accidents and undetermined origin.

The data is from "A LOOK AT THE DEATHS OF THOSE INVOLVED"
written by Jim Marrs and Ralph Schuster
http://www.assassinationresearch.com/v1n2/deaths.h...

The following comment on the deaths of assassination witnesses appeared at the end of the movie "Executive Action," released in 1973, starring Burt Lancaster and Robert Ryan:

"In the three-year period which followed the murder of President Kennedy and Lee Harvey Oswald, 18 material witnesses died - six by gunfire, three in motor accidents, two by suicide, one from a cut throat, one from a karate chop to the neck, three from heart attacks and two from natural causes".

"An actuary, engaged by the "London Sunday Times," concluded that on November 22, 1963, the odds against 18 witnesses being dead by February 1967, were one hundred thousand trillion to one".


But in a reply to the 1977 House Select Committee on Assassinations, the Times editor tried to refute the probability calculation:
"He was asked what were the odds against 15 named people out of the population of the United States dying within a short period of time, to which he replied -correctly - that they were very high. However, if one asks what are the odds against 15 of those included in the Warren Commission Index dying within a given period, the answer is, of course, that they are much lower. Our mistake was to treat the reply to the former question as if it dealt with the latter - hence the fundamental error in our first edition report, for which we apologize".

THERE WERE 42 DEATHS (33 UNNATURAL)IN THE THREE YEARS AFTER THE ASSASSINATION.

Marrs and Schuster conclude: "The House Committee made little or no attempt to seriously study the number of deaths which followed the JFK assassination."

The original probability calculation as stated was correct.

In any case, the Times Editor did not consider DEATH BY UNNATURAL CAUSES. He never calculated the probability of 15 UNNATURAL witness deaths out of approximately ONE THOUSAND witnesses within just ONE year of the assassination.

The probability is 1 in 21,230 TRILLION!
It is the same order of magnitude as the original calculation

Assuming there were 1,000 witnesses, the probability that at least 15 would die UNNATURAL deaths in the year following the assassination is 1 in 21,230 trillion.

Assuming there were 10,000 witnesses, the probability that at least 15 would die UNNATURAL deaths in the year following the assassination is 1 in 1,000

It's not likely that the 15 deaths were coincidental.

For the odds of death in each category, I used this table of 1999 mortality data:
http://www.nsc.org/lrs/statinfo/odds.htm

Probability of:
........................1 year...Lifetime
suicide.................0.000107 0.008197
homicide................0.000062 0.004739
accidental death........0.000359 0.027778
undetermined death......0.000014 0.001101

Total...................0.000542 0.041815
The probability of an unnatural death is the sum of the probabilities

The Poisson Distribution

Although the Normal (Gaussian) probability distribution is by far the most important, there is another which has proven to be particularly useful - the Poisson Distribution. It is derived from and a special case of the Normal Distribution.

The Poisson Distribution applies when the probability "P" for success in any one trial is very small, but the number of trials N is so large that the expected number of successes (a=pN) is a moderate sized quantity.

The probability of m deaths: P(m) =a**m*exp(-a)/m!
In words, the Probability of EXACTLY m successes = a to the m'th power times the exponential function of (-a), divided by m factorial.
m! -15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1

Now lets use Poisson to determine the probability of a given number of witnesses meeting unnatural deaths within a year of the JFK assassination. The only assumption we are making is the number of witnesses.

Assume N= total witnesses = 1000
Let p= Probability of dying from UNNATURAL causes in a given year = 0.000542
Let a= Expected number of unnatural deaths = pN= 0.542
Let m= Actual number of unnatural deaths = 15

Then probability P(m) of exactly m=15 UNNATURAL deaths within a given year out of a predefined group of N = 1000 witnesses is:
P(m) =a**m*exp(-a)/m! or p(15)= 0.542**15*exp(-.542)/15!

Here are the probabilities for m=1 through m=15 deaths.
Prob(X=m) = probability of EXACTLY m DEATHS
Prob(X>=m) = probability of at AT LEAST m DEATHS (the one we want)

m Prob(X=m) Prob(X>=m)
1 3.15E-01 4.18E-01 Prob (X>=1 death)= 0.418
2 8.54E-02 1.03E-01
3 1.54E-02 1.78E-02
4 2.09E-03 2.34E-03
5 2.27E-04 2.49E-04 Prob (X>=5)= 1 in 4000
6 2.05E-05 2.22E-05
7 1.59E-06 1.70E-06
8 1.07E-07 1.14E-07
9 6.47E-09 6.84E-09
10 3.51E-10 3.69E-10 Prob (X>=10) = 1 in 2.8 billion
11 1.73E-11 1.81E-11
12 7.80E-13 8.14E-13
13 3.25E-14 3.38E-14
14 1.26E-15 1.31E-15
15 4.55E-17 4.71E-17 Prob (X>=15) = 1 in 21,230 trillion

For 15 or more deaths, the probability is:
Prob (X>=15) = 4.71e-17 = 0.000000000000000047101810079330
or 1 out of 21,230,606,601,227,800

Check the graph for a probability sensitivity analysis
Assume there were 10,000 witnesses.
The probability that at least 15 would die an unnatural death within one year is
P= .00096 = 9.6E-04 (1 in 1,000).



POISSON(x,mean,cumulative)
X is the number of events.

Mean is the expected numeric value.
Cumulative is a logical value that determines the form of the probability distribution returned.

If Cumulative is TRUE, POISSON returns the cumulative Poisson probability that the number of random events occurring will be between zero and x inclusive;
if FALSE, it returns the Poisson probability mass function that the number of events occurring will be exactly x.