# Multiplication rule for "AND"

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**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?**Independent Events VS. Dependent Events**- 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* - 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*

- One card is drawn from a standard deck of 52 cards and is not replaced. A second card is then drawn.
- 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.