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JFK Assassination: Mathematical Proof of a Grassy Knoll Shooter

JFK Assassination: Mathematical Proof of a Grassy Knoll Shooter

Richard Charnin
Feb 5, 2014
Updated: June 8, 2014

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The corporate media never discusses the HSCA conclusion of a probable conspiracy based on overwhelming eyewitness testimony and scientific acoustic evidence of shooters at the Grassy Knoll. Warren Commission apologists are relentless in their shameless promotion of the ridiculous, discredited Lone Nut Gunman and Single Bullet Theory.

The General Problem
1) n witnesses claim they heard, saw or smelled shots from the Grassy Knoll
2) P is a probability estimate that a given witness would be correct
3) Witness observations are independent events
4) The probability PM that a given witness is MISTAKEN: PM = 1 – P
5) The probability PA that ALL n witnesses are MISTAKEN: PA = PM^n

This is an update to the original post which is referenced in

Dealey Plaza witness survey data is in the JFKCalc spreadsheet:

This article discusses the importance of independent, corroborating witness evidence in a court of law.

My adjusted survey, which includes witnesses cited by Feldman and Galanor, indicates that at least 93 heard or saw shots fired from the Grassy Knoll; 45 said the TSBD.

Researcher Harold Feldman wrote that of 121 eyewitnesses: 51 (42%) said shots came from the Grassy Knoll area, 32 from the TSBD, and 38 had no opinion.

Given P = 0.42 is probability of a witness being correct in stating that shots came from the Knoll, then the probability PM = 0.58 = 1-.42 that the witness was mistaken.The joint probability PA that ALL 51 witnesses were mistaken and there was NOT a Grassy Knoll shooter is 0.58 to the 51st power.
PA = 0.58^51 = 8.6E-13 = 0.000000000000861 or of 1 in 1,161,909,568,739 or 1 in 1.16 trillion.

Therefore, the probability PS that there was a Grassy Knoll shooter is PS = 1-PA = 0.999999999999139

If we exclude the 38 witnesses who had no opinion as to the origin of the shots, then 51 of 83 (62%) said shots came from the Grassy Knoll and there is a 38% probability that a given witness would be mistaken. The probability that ALL 51 witnesses would be mistaken is much lower: PA = 0.38^51 = 3.71E-22
PA= 1 in 2,697,966,622,402,536,000,000 or 1 in 2.7 billion trillion!

Of course, if just ONE witness was correct in observing a shot from the Grassy Knoll, then all 51 were correct. Therefore, the Warren Commission’s conclusion that Lee Harvey Oswald was a Lone Gunman shooting from the Texas Book Depository was bogus.

Summary of Surveys

Survey..........Feldman McAdams Galanor Adjusted

Total Asked…………121 241 216 223
Total Opinions……….83 100 110 133
Grassy Knoll…………51. 35. 52. 84
Book Depository…….32. 61. 48. 36
Both TB and GK………0.. 2.. 5.. 9
Other locations………..0.. 2.. 4.. 4
No opinion……………38. 69. 37. 36
Not asked……………..0. 72. 70. 54

GK % of Opinions……61. 35. 47. 63
TB % of Opinions……39. 61. 44. 27
Probability ALL GK witnesses mistaken:
Probability……….E-22 E-07 E-17 E-43

John McAdams
Of 241 total witnesses, 102 had an opinion on the origin of the shots. Sixty-three (63) said they came from the TSBD and 37 from the Grassy Knoll.  The probability that ALL  37 witnesses were mistaken in claiming that shots came from the Grassy Knoll is 3.76E-08 or 1 in 26 million!

Stewart Galanor
How the Warren Commission and the House Select Committee on Assassinations
minipulated evidence to dismiss witness accounts of the assassination.

Of the 216 interviewed, 52 heard at least one shot from the knoll, 48 from the TSBD, 5 from both locations, 4 elsewhere. The probability PA that 52 witnesses who said shots were fired from the Grassy Knoll would ALL be MISTAKEN is E-17 (1 in 100,000 trillion).

Adjusted Totals
A total of 224 witnesses were asked where the shots came from. Of the 133 who had an opinion, 84 said the Grassy Knoll; 36 said the TSBD; 9 both locations; 4 said elsewhere, 37 had no opinion.

The probability analysis was posted in and elicited the following comments:

Acoustic Evidence
In 1978 at the HSCA, an analysis of gunshots recorded on a DPD dictabelt was presented by engineers from Bolt, Beraneck and Newman. The study indicated that there was a 96% probability that at least 6 sharp impulses occurred at 12:30 – the exact time of the shots. At least three were from in front of the limo at the Grassy Knoll. The evidence forced the HSCA to conclude that the assassination was “probably” a conspiracy. It was a “limited hangout”. There has been no follow-up investigation.

Sounds of Silence
“The conclusion of four separate shots coincides with 4 impacts visible in the Z-film. The acoustic impulses were retested in a 2001 investigation (‘Echo Correlation Analysis and the Acoustic Evidence in the Kennedy Assassination Revisited’) by D.B. Thomas, published in the Journal Science and Justice, Vol. 41, p. 21. The impulses are shown below, with the four highest amplitude peaks associated with rifle muzzle blasts.

The hypergeometric p-function was used for differing weighting factor distribution sets, H{M..N, n, i} to assess significance or likelihood of occurrence. It’s based on the no. of echo ‘windows’ M, with each spanning 190msec (total time) at 2msec width per window and n for assigned impulses in the evidence pattern, with ‘i’ the “coincident impulses” or those matching the original (11/22/63)evidence and the test result. The question was whether a succession of first impulses of given amplitude could be manifesting a signal or was merely random noise.

Thomas found that for a given configuration for 2 motorcycles at designated locations, 1 for (GK) shooter location and one for alignment of muzzle blasts with one pair of echoes, the p -value is 0.000012 or about 1 in 100,000 against the null hypothesis, i.e. that the impulses were from random noise. An alternative way to put this is that the odds are 100,000 to 1 in favor of the impulses comprising actual rifle shots.”

David Lifton: #5 man
In 1965, assassination researcher and author David Lifton (“Best Evidence”) analyzed the famous Mary Moorman photo. He discovered a figure holding an object behind the fence on the Grassy Knoll. The image was the fifth, final and clearest image of the subject identified in the photo. Later, the figure was identified as a man by 10 independent photographic experts. Each signed statements to that effect and none were told that the photo was taken in Dealey Plaza.


Posted by on February 5, 2014 in JFK


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