Definition of conditional probability

con_prob

What is the relationship in terms of set theory between conditional probability and Bayes’ theorem?

Pebble World Intuition

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Thinking about the last step in this problem and how it relates to the formula in Bayes law?

Thinking about multidimensional spaces?

Formal Definition of Bayes Law and multiple events

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Again thinking about connection between conditional probabiliy and Bayes Theorem.

LOTP

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LOTP Intuition

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Some notes on 3 Blue 1 Brown Video

https://www.youtube.com/watch?v=HZGCoVF3YvM

Steve is very shy and withdrawn, invariably helpful but with very little interest in people or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.

Upon hearing this most people thought that this description matches a librarian not a farmer, but the idea is that this is irrational.

One needs to take into account the ratio of librarians to farmers.

Bayes theorem is for when you have a hypothesis and some evidence and you want to calculate the probability that this hypothesis is true given the evidence. P(Hypotheis|Evidence), P(H|E)

So the first term, P(H), is that the hypothesis holds before you consider any evidence. This number is known as the prior.

The second term in the numerator is known as the “likelihood”. P(E|H), the probability of seeing the evidence give that the hypothesis is not true.

At this point, I think I need to spend some time coming up wiht my own example so I can derive the problem like is done in the video. Maybe use a sample of 10 instead of 100 and work through the problem.