Conditional probability and set notation

What you'll learn

1. 1

   Imagine you have a bag of 5 red and 3 blue marbles. If you pick one marble without looking, what's the chance it's red? That's a simple probability.

2. 2

   Let's explore with marbles. Drag the marbles to see all the possible pairs when you pick two marbles without replacement.

3. 3

   We want P(second marble is red | first marble was red). That means: given the first was red, what's the chance the second is also red?

4. 4

   If the first marble picked is blue, how many marbles are left in total?

5. 5

   Now try this: you have 4 green and 2 yellow marbles. Pick one, then another without looking. Given the first is green, what's P(second is green)?

6. 6

   Let's write it using set notation. P(A|B) means 'probability of A given B'. For our marble example: A = 'second marble is red', B = 'first marble is red'.

7. 7

   Using the formula P(A|B) = P(A and B) / P(B), if P(A and B) = 0.3 and P(B) = 0.6, what is P(A|B)?