113 Math
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

  • statistics
  • probabilities