math

By Jaclyn KogutBy Jaclyn Kogut

Objectives �Objectives �

Determine whether events are independent or dependent.

Find the probability of independent and dependent events.

Determine whether events are independent or dependent.

Find the probability of independent and dependent events.

VocabularyVocabulary

Independent events:

Dependent events:

Independent events:

Dependent events:

The occurrence of oneevent that does notaffect the probability ofthe other

The occurrence of oneevent that affects theprobability of the otherConditional Probability

The occurrence of oneevent that does notaffect the probability ofthe other

The occurrence of oneevent that affects theprobability of the otherConditional Probability

Conditional ProbabilityConditional Probability

When finding the probability of dependent events, you use conditional probability.

P(BA) = the probability of event B, given that event A has already occurred

When finding the probability of dependent events, you use conditional probability.

P(BA) = the probability of event B, given that event A has already occurred

Probability of Independent Events

Probability of Independent Events

If A and B are independent events, then

P(A and B) = P(A) P(B)

If A and B are independent events, then

P(A and B) = P(A) P(B)

Example 1: Finding the Probability of Independent

Events

Example 1: Finding the Probability of Independent

Events

There is a ten-sided cube: three sides are colored green, two sides are colored red, and five sides are colored blue

Find the probability of rolling a green, then red, then blue

There is a ten-sided cube: three sides are colored green, two sides are colored red, and five sides are colored blue

Find the probability of rolling a green, then red, then blue

Example 1: Finding the Probability of Independent

Events

Example 1: Finding the Probability of Independent

Events

P(green, then red, and then blue) = P(green) P(red) P(blue)

P(green, then red, and then blue) = P(green) P(red) P(blue)

Example 1: Finding the Probability of Independent

Events

Example 1: Finding the Probability of Independent

EventsStep 1: Find the probability of rolling one green side

P(green) = 3/10

Step 2: Find the probability of rolling one red side

P(red) = 2/10 = 1/5

Step 3: Find the probability of rolling one blue side

P(blue) = 5/10 = 1/2

Example 1: Finding the Probability of Independent

Events

Example 1: Finding the Probability of Independent

EventsStep 4: Multiply each separate probability by

each other

P(green, then red, and then blue) = P(green) P(red) P(blue)

= 3/10 1/5 1/2 = 3/100

= 0.03 probability

Step 4: Multiply each separate probability by each other

P(green, then red, and then blue) = P(green) P(red) P(blue)

= 3/10 1/5 1/2 = 3/100

= 0.03 probability

Probability of Dependent Events

Probability of Dependent Events

If A and B are dependent events, then

P(A and B) = P(A) P(BA), where

P(BA) is the probability of B, given that A has already occurred

If A and B are dependent events, then

P(A and B) = P(A) P(BA), where

P(BA) is the probability of B, given that A has already occurred

Example 2: Finding the Probability of Dependent

Events

Example 2: Finding the Probability of Dependent

Events Two number cubes are rolled - one

blue and one white. Explain why the events are dependent and find the probability.

The blue cube must show a 5 and the sum of the two cubes must be greater than 8

Two number cubes are rolled - one blue and one white. Explain why the events are dependent and find the probability.

The blue cube must show a 5 and the sum of the two cubes must be greater than 8

Example 2: Finding the Probability of Dependent

Events

Example 2: Finding the Probability of Dependent

Events

P(blue 5 and sum 8) = P(blue 5) P(sum 8blue 5)

P(blue 5 and sum 8) = P(blue 5) P(sum 8blue 5)

Example 2: Finding the Probability of Dependent

Events

Example 2: Finding the Probability of Dependent

EventsStep 1: Find the probability of blue rolling a

3

P(blue 5) = 2/12 = 1/6

Step 2: Find the probability of the white cube rolling a number that will make the sum greater than 8

P(sum 8 blue 5) = 4/6 = 2/3

Step 1: Find the probability of blue rolling a 3

P(blue 5) = 2/12 = 1/6

Step 2: Find the probability of the white cube rolling a number that will make the sum greater than 8

P(sum 8 blue 5) = 4/6 = 2/3

Example 2: Finding the Probability of Dependent

Events

Example 2: Finding the Probability of Dependent

EventsStep 3: Multiply each probability together

to get the final probability

P(blue 5 and sum 8) = P(blue 5) P(sum 8blue 5)

= 1/6 2/3 = 2/18 = 1/9 = .11111111111

probability

Step 3: Multiply each probability together to get the final probability

P(blue 5 and sum 8) = P(blue 5) P(sum 8blue 5)

= 1/6 2/3 = 2/18 = 1/9 = .11111111111

probability

Determine if the event is independent or

dependent:

Determine if the event is independent or

dependent: Selecting a spade when the first card is taken out of the deck

Drawing a queen, putting it back, and then drawing a king

Eating all the red skittles and taking out a green skittle

Taking out all the green skittles, putting 5 back, eating a purple, and finding a orange skittle

Selecting a spade when the first card is taken out of the deck

Drawing a queen, putting it back, and then drawing a king

Eating all the red skittles and taking out a green skittle

Taking out all the green skittles, putting 5 back, eating a purple, and finding a orange skittle