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Yay! You’ve got people talking about probability on here. I love it.I plugged into a few different programs, 5 Pieces of evidence in the Kohberger case and the odds of them all occurring and BK being innocent.
Below you can see the odds that this program assigned to each event, which was the most conservative one I used.
Notice how I didn’t mention the DNA.
1. Ownership of the same type of car.
2. Driving at a time consistent with him being the killer.
3. Powering down his phone throughout the murder window.
4. Purchasing the same model knife and sheath, which are now missing.
5. Seeking to purchase the same model knife and sheath, beginning two days following the murders.
Combining the Probabilities
To estimate the odds of innocence, we consider the likelihood that all these events occur together by chance for an innocent person. In probability theory, if events are independent, their joint probability is the product of their individual probabilities. While these events are not entirely independent (e.g., owning a knife and searching for it are related), we can use rough estimates to illustrate the cumulative effect:
Car: ~1/100 (0.01)
Driving at 4 a.m.: ~1/50 (0.02)
Phone powered down: ~1/50 (0.02)
Owning and missing knife: ~1/5,000 (0.0002)
Searching for knife post-murder: ~1/10,000 (0.0001)
If we assume approximate independence for simplicity, the joint probability is:
0.01×0.02×0.02×0.0002×0.0001=8×10−120.01 \times 0.02 \times 0.02 \times 0.0002 \times 0.0001 = 8 \times 10^{-12}0.01 \times 0.02 \times 0.02 \times 0.0002 \times 0.0001 = 8 \times 10^{-12}
This translates to a 1 in 125 billion chance that an innocent person would match all these criteria by coincidence. Even if we adjust for partial dependence (e.g., knife ownership and searching being related), the combined probability remains extraordinarily low, likely on the order of 1 in millions.
The following is for those of you whose eyes glaze over or stomachs churn whenever you see math, but you want to understand MassGuy’s post.
First, a quick review of some basics:
Convert a probability from fraction form to decimal form by dividing the top number (the numerator) by the bottom number (the denominator). For example, 1/4 = 1 divided by 4 = 0.25.
Convert a decimal to a percent by multiplying by 100 (that is, move the decimal point right two places) and adding the percent symbol. For example, 0.25 = 25%.
Find the probability of two or more independent events by multiplying their probabilities (written in decimal or fraction form only, not percent form). To understand why, check out this explanation in Khan Academy:
Khan Academy
(Pro tip: To understand math, you must have paper and pencil in hand and work the examples.)
So the probability of ALL five of MassGuy’s events happening at the same time is;
0.01×0.02×0.02×0.0002×0.0001 = 8×10⁻¹⁴ (in scientific notation) = 0.00000000000008 (in decimal form) = 0.000000000008% (in percent form).
That is a very low probability! (But still not as low as the probability that the DNA on the knife sheet belongs to anyone other than Bryan Kohberger).