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Get Started Now- Lesson: 16:01
- Lesson: 2a11:27
- Lesson: 2b11:26
- Lesson: 319:07

$\cdot$ 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*) = $\frac{P(A\;and \;B)}{P(A)}$

$\cdot$ recall: P(

then: P(

- 1.
**Definition of Conditional Probability**

$\cdot$ P(): probability of event*B | A*occurring, given that event*B*has already occurred.*A*

$\cdot$ recall: P(and*A*) = P(*B*) $\cdot$ P(*A*)*B | A*

then: P() = $\frac{P(A\;and \;B)}{P(A)}$*B | 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.

a)Find the probability that a red ball is selected.b)Given that the ball selected is red, find the probability that it came from Bag A. - 3.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.

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