Email email@example.com to sign up to receive news and updates
Boole Probability Example
Boole is well known for so-called Boolean algebra. However, his almost totally forgotten work in how the mind works, logic, and probability and statistics, his An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, is worth a read.
I wanted to show an example of his thinking in the "simplest" case. Consider
- x is a proposed hypothesis, and prob(x) = a
- y is a phenomenon which might occur because of x's consequences
- y has been observed
- prob(xy) = ap
Note that a is the a priori probability of the hypothesis, and p is the probability of y given x is true.
Putting this all together,
P = prob(xy)/prob(y) = ap/prob(y), and is the a posteriori probability of the physical hypothesis.
This can be simplified to
P = ap/(ap + c(1-a))
Note that the term c is the probability that if x does not occur, y occurs.
Please see this spreadsheet for an example where you can play with the numbers and see how the probabilities change.
Please check out the following books
Thanks for reading!
Please anonymously VOTE on the content you have just read:Like:
If you enjoyed any of my content, please consider supporting it in a variety of ways:
- PLEASE take a moment to check out two GoFundMe fundraisers I set up. The idea is to make it possible for me to pursue my passions. My goal is to be able to create free randomized educational worksheets and create poetry on a full-time basis. THANK YOU for your support!
- Email firstname.lastname@example.org to sign up to receive news and updates
- Donate any amount via PayPal
- Take my Five Poem Challenge
- Subscribe to my YouTube channel
- Visit my Amazon author page
- Buy what you need on Amazon using my affiliate link
- Follow me on Twitter here
- Buy ad space on Statisticool.com
AFFILIATE LINK DISCLOSURE: Some links included on this page may be affiliate links. If you purchase a product or service with the affiliate link provided I may receive a small commission (at no additional charge to you). Thank you for the support!