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Objective

Find the probability of independent and dependent events

Vocabulary

Compound Event

An event that consists of two or more simple events

Vocabulary

Independent Events

Two or more events in which the outcome of one event does not affect the outcome of the

other event(s)

Vocabulary

Dependent events

Two or more events in which the outcome of one event does affect the outcome of the other

event(s)

Example 1 Probability of Independent Events

Example 2 Use Probability to Solve a Problem

Example 3 Probability of Dependent Events

The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?

1/3

Write probability statement for the 1st spinner

P(greater than 6) =

Write the formula for probability

Numbers greater than 6 Total Numbers

The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?

1/3

P(greater than 6) =

Count the numbers greater than 6 for the numerator

Numbers greater than 6 Total Numbers

P(greater than 6) = 3

The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?

1/3

P(greater than 6) =

Count the total numbers for the denominator

Numbers greater than 6 Total Numbers

P(greater than 6) = 3 10

The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?

1/3

The second spinner is exactly like the 1st spinner except for color so same probability

P(greater than 6) = 3 10

P(greater than 6) = 3 10

The two spinners below are spun. What is the probability that both spinners will show a number greater than 6?

1/3

Write the probability statement for both spinners

P(greater than 6) = 3 10

P(greater than 6) = 3 10

P(both spinners greater than 6) =

Multiply the probability of each spinner

3 10

3 10

Use calculator to multiply

P(both spinners greater than 6) = 9 100

Answer:

NOTE: Independent event since neither spinner affected the other

The two spinners below are spun. What is the probability that both spinners will show a number less than 4?

Answer: P (both spinners less than 4) =

1/3

What is the probability that a student picked at random will be an eighth-grade girl?

Girls

Boys

Cross River Middle School

Grade 8

Grade 7

Grade 6

Fraction of the Population

Demographic Group

2/3

Write probability statement for an eighth-grade girl

P(8th grade girl) =

What is the probability that a student picked at random will be an eighth-grade girl?

Girls

Boys

Cross River Middle School

Grade 8

Grade 7

Grade 6

Fraction of the Population

Demographic Group

2/3

Note: Data is given in fractions which can be used as a probability!

P(8th grade girl) =

What is the probability that a student picked at random will be an eighth-grade girl?

Girls

Boys

Cross River Middle School

Grade 8

Grade 7

Grade 6

Fraction of the Population

Demographic Group

2/3

Write probability of 8th grade

P(8th grade girl) =

Put multiplication sign

Write probability of girl

What is the probability that a student picked at random will be an eighth-grade girl?

Girls

Boys

Cross River Middle School

Grade 8

Grade 7

Grade 6

Fraction of the Population

Demographic Group

2/3

Multiply

P(8th grade girl) =

P(8th grade girl) =Answer:

NOTE: Independent event since neither probability affected the other probability

POPULATION Use the information below. What is the probability that a student picked at random will be a sixth grade boy?

Answer:

Girls

Boys

Monterey Middle School

Grade 8

Grade 7

Grade 6

Fraction of the Population

Demographic Group

Probability (6th grade boy) =

2/3

There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen.

3/3

Since the sock is not put back, it will affect the probability of the second sock chosen

This is a dependent event

Write probability statement for the first sock chosen

P(1st sock blue) =

There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen.

3/3

Numerator is number of blue socks

This is a dependent event

P(1st sock blue) = 6

Denominator is total number of socks in drawer

18

There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen.

3/3

This is a dependent event

P(1st sock blue) = 6 18

Write probability statement for the second sock chosen

P(2nd sock blue) =

Numerator is number of blue socks minus the one not replaced

5

Denominator is total number of socks in drawer minus the one not replaced

17

There are 4 red, 8 yellow, and 6 blue socks in a drawer. Once a sock is selected, it is not replaced. Find the probability that two blue socks are chosen.

3/3

This is a dependent event

P(1st sock blue) = 6 18

Write probability statement for both socks

P(2nd sock blue) = 5 17

P(both socks blue) =

Multiply the two probabilities of the 2 socks chosen

Multiply

P(both socks blue) =Answer:

There are 6 green, 9 purple, and 3 orange marbles in a bag. Once a marble is selected, it is not replaced. Find the probability that two purple marbles are chosen.

Answer: P (two purple marbles) =

*

3/3

Assignment

Lesson 8:5Probability of Compound

Events4 - 26 All