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2. Find the probability of getting at least 2 heads when. tossing a coin 3 times. 1. You have 6 movies. You want to watch one now, and a different one later. How many ways can you choose two movies to watch?. Bell Work. There are 30 ways to choose the movies.

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bell work

2. Find the probability of getting at least 2 heads when

tossing a coin 3 times.

1. You have 6 movies. You want to watch one now, and a different one later. How many ways can you choose two movies to watch?

Bell Work

There are 30 ways to choose the movies.

Hint: Make a tree diagram to list the outcomes, or sample space, of the experiment. Circle the successful outcomes.

slide2

Because 4 of the 8 outcomes have at least 2 heads,

, or

the probability is

4

1

First

8

2

Second

Third

EXAMPLE 3

Answer:

slide3

Using the Fundamental

Counting Principle

slide4

Name three different ways to organize your results from flipping a coin twice

Table

Organized List

( H,H )

( H, T )

( T, H )

( T, T )

H T

Tree Diagram

H

T

H

T

H

T

H

T

slide5

EXAMPLE 1

Making a Tree Diagram

You can make a tree diagram to count the number of possible outfits you could wear if you had 4 shirts to choose from and 3 different pants to choose from.

There are 12 different possible outfits.

Is there an easier way?

You decide to include socks as part of the outfit . You can choose between red (R) and green (G). How many outfits are possible now?

You have 4 shirts, 3 pants and 2 socks to select.

The number of possible outfit are 4 x 3x 2 = 24 outfits.

slide6

To build a skateboard, you can choose one deck and one type of wheel assembly from those shown. To count the number of different skateboards you can build, use the counting principle.

5 x 3 = 15

decks

wheel assemblies

EXAMPLE 2

Using the Counting Principle

You can build 15 different skateboards.

slide7

26 26 26 10 10 = 1,757,600

letters

digits

Using the Counting Principle

Your soccer team’s uniform choices include yellow and green shirts, white, black, and green shorts, and three colors of socks. How many different uniforms are possible?

Hint : The soccer team has 2 shirts 3 shorts and 3socks to select. Use the counting principle.

The number of possible uniforms are 2 x 3x 3= 18 uniforms

Let’s try a tough one!

You are choosing a password that starts with 3 letters and then has 2 digits. How many different passwords are possible?

There are 1,757,600 different possible passwords.

slide8

24 25 25 10 10 = 1,500,000

letters

digits

Try this one!

In the last example,suppose that the passwords may not start with an A or use the letter Q. How many different passwords are possible using three letters and then two numbers? Explain.

Hint: There are 24 choices for the first letter, 25 for each of the next two letters, and 10 for each of the digits.

There are 1, 500, 000 different possible passwords.

slide9

There are 26choices

for each of the 3letters.

There are 10 choices for

each of the 4 digits.

The standard New York state license plate has 3 letters followed by 4 digits. How many different license plates are possible if the digits and letters can be repeated?

26 26 26 10 10 10 10

=

175,760,000

You Try:

EXAMPLE 2

There are 175,760,000 different license plates possible.

slide10

The standard New York state license plate has 3 letters followed by 4 digits. How many different license plates are possible if the letters cannot be repeated?

26 x 25 x 24 x 10 x 10 x 10 x 10

There are 156,000,000different license plates possible.

slide11

Five runners are sprinting the 100 meter dash. How many different ways can they finish?

5 x 4 x 3 x 2 x 1

120 different ways

slide12

George guessed the answers on five multiple choice questions on his test. Each question had three choices. How many different answer combinations were there?

3 x 3 x 3 x 3 x 3 = 243 different combinations

What is the probability that George will get all of those questions correct?

1/3 x 1/3 x 1/3 x 1/3 x 1/3 = 1/243 or .0041

This is less than a 1% chance so don not guess on multiple choice test : )

slide13

1

=

P(1234)

10,000

10 10 10 10

=

10,000

EXAMPLE 3

Solving a Multi-Step Problem

You are assigned a computer-generated 4- digit password to access your new voice mail account. If the digits can be repeated, what is the probability that your assigned password is 1234?

Use the counting principle to find the total number of different passwords.

STEP 1

STEP 2

Find the number of favorable outcomes.

Only one outcome is 1234.

STEP 3

Find the probability that your password is 1234.

or 0.0001.

slide14

Practice:

Fundamental Counting Principle Worksheet