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113 Math

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113.038.10 Probability - Bayes Theorem

# Bayes Theorem

The probability of event A given some new evidence B

- $$P(A | B) = \frac{P(B | A) * P(A)}{P(B)}$$

- Denominator can be read as "total probability of B":

- Use trimmed trees if you need a visual. E.g.
- Given 2 coins, one fair, one with 2 sides of heads
- What is the likelihood of a heads from the fair coin?
- Flip 1
- Fair coin = 2 outcomes, 1 heads, 1 tails
- Unfair coin = 1 outcome, 2 heads
- If the result is heads, we remove tails from the outcome set b/c we know it could only happen with the fair coin.
- Then we take our one result and divide by the total number of outcomes left, in this case 3.
- So the probability of getting a fair heads in this case is 1/3

##### Tags:

- statistics
- probabilities