# Conditional probability #### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered. #### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals. #### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now! ##### Intros
###### Lessons
1. Definition of Conditional Probability
$\cdot$ 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) = $\frac{P(A\;and \;B)}{P(A)}$
##### Examples
###### Lessons
1. 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.
1. Find the probability that a red ball is selected.
2. Given that the ball selected is red, find the probability that it came from Bag A.
2. It is known that 60% of graduating students are girls. Two grads are chosen at random. Given that at least one of the two grads are girls, determine the probability that both grads are girls.
###### Topic 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) = $\frac{P(A\;and \;B)}{P(A)}$