Conditional probability
Conditional probability
Lessons
Notes:
$\cdot$ P(B  A): probability of event B occurring, given that event A has already occurred.
$\cdot$ recall: P(A and B) = P(A) $\cdot$ P(B  A)
then: P(B  A) = $\frac{P(A\;and \;B)}{P(A)}$

2.
Probability Tree Diagram
Bag A contains 2 red balls and 3 green balls. Bag B contains 1 red ball and 4 green balls.
A fair die is rolled: if a 1 or 2 comes up, a ball is randomly selected from Bag A;
if a 3, 4, 5, or 6 comes up, a ball is randomly selected from Bag B.