Bayesian Probability

Probability intuition sheet

1. Prior → evidence → posterior

Start with an estimate, receive evidence, judge its strength, then update.

2. Evidence quality matters

Ask whether the evidence is relevant, reliable, comparable, and independent.

3. Probability is not impact

A 5% chance of losing 35% of revenue combines:

$$0.05 \times 0.35 = 1.75\%$$

But expected loss does not fully describe the severe downside scenario.

4. Conditional probability changes the sample space

$$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$

The event after the bar determines the group you focus on and therefore the denominator.

5. Do not reverse conditions

$$P(A\mid B)\neq P(B\mid A)$$

In our example:

$$P(\text{high IRR}\mid\text{successful manager})=60\%$$

while:

$$P(\text{successful manager}\mid\text{high IRR})=37.5\%$$