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- Lesson: 3b9:40
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$\cdot$ 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(

- 1.
**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**. - 2.
**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? - 3.
**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* - 4.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?

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