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Get Started Now- Intro Lesson3:38
- Lesson: 17:48
- Lesson: 2a13:41
- Lesson: 2b9:40
- Lesson: 3a5:08
- Lesson: 3b3:09

$\cdot$ P(*A* and *B*): probability of event *A* occurring and then event *B* occurring **in successive trials**.

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

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

$\cdot$ Independent Events

If the events*A, B* are independent, then the knowledge that event *A* has occurred has no effect on the probably of the event *B* occurring, that is P(*B | A*) = P(*B*).

As a result, for independent events: P(*A* and *B*) = P(*A*) $\cdot$ P(*B | A*)

= P(*A*) $\cdot$ P(*B*)

$\cdot$ P(

$\cdot$ P(

$\cdot$ Independent Events

If the events

As a result, for independent events: P(

= P(

- Introduction
**P(**and*A*) VS. P(*B*or*A*)*B*

P(and*A*): probability of event*B*occurring and then event*A*occurring*B***in successive trials**.

P(or*A*): probability of event*B*occurring or event*A*occurring*B***during a single trial**. - 1.
**Multiplication Rule for "AND"**

A coin is tossed, and then a die is rolled.

What is the probability that the coin shows a head and the die shows a 4? - 2.
**Independent Events VS. Dependent Events**a)One card is drawn from a standard deck of 52 cards and is not replaced. A second card is then drawn.

Consider the following events:

= {the $1^{st}$ card is an ace}*A*

= {the $2^{nd}$ card is an ace}*B*

Determine:

$\cdot$ P()*A*

$\cdot$ P()*B*

$\cdot$ Are eventsdependent or independent?*A, B*

$\cdot$ P(and*A*), using both the tree diagram and formula*B*b)One card is drawn from a standard deck of 52 cards and is replaced. A second card is then drawn.

Consider the following events:

= {the $1^{st}$ card is an ace}*A*

= {the $2^{nd}$ card is an ace}*B*

Determine:

$\cdot$ P()*A*

$\cdot$ P()*B*

$\cdot$ Are eventsdependent or independent?*A, B*

$\cdot$ P(and*A*), using both the tree diagram and formula*B* - 3.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)What is the probability of selecting a green ball from Bag A?b)What is the probability of selecting a green ball?

9.

Probability

9.1

Introduction to probability

9.2

Determining probabilities using tree diagrams and tables

9.3

Probability of independent events

9.4

Probability with Venn diagrams

9.5

Addition rule for "OR"

9.6

Multiplication rule for "AND"

9.7

Conditional probability

9.8

Probability with permutations and combinations

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