Bayes' Theorem is a fancy way of saying "Hey, I'm not that good at probability, but I'll just make something up and hope it works out."
So, P(A|B) = P(B|A) * P(A) / P(B). Yeah, that's it. Just multiply and divide some numbers, voila! You're a certified statistician.
Example:
Let's say you have a 50% chance of getting a free donut at the office. And let's say 70% of people who get a free donut are happy. And let's say 90% of people who are happy have a 50% chance of getting a free donut. What's the chance you'll get a free donut if you're happy?
P(A|B) = P(B|A) * P(A) / P(B) = 0.7 * 0.5 / 0.5 = 0.7
So, there's a 70% chance you'll get a free donut if you're happy! Woohoo! Now, go forth and calculate the probability of getting a free cat!
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