Lesson 3 of 14

Conditional Probability

Updating probabilities on new information, independence, and the two-children puzzle.

The definition

Conditioning restricts the sample space to what you know happened:

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

Read: among the worlds where $B$ occurred, what fraction also have $A$ ? Rearranged, the multiplication rule $P(A \cap B) = P(A \mid B)\,P(B)$ builds joint probabilities from chains of conditionals, which is the natural way to handle sequential experiments (draws without replacement, multi-stage games).

Keep reading with a free account

Every lesson and every problem on Quant Engine is free. Making an account takes 30 seconds and no card. Then you can read the rest of this lesson, take the checkpoint and keep your progress.

Create a free account Log in