The table in the 'show your work' section shows the results of a telephone survey asking adults if they intended to make online purchases in the next month.

Fill in the missing information:

Ask me to check your answers before you proceed.

The table in the 'show your work' section shows the results of a telephone survey asking adults if they intended to make online purchases in the next month.

Create a Venn Diagram to match the situation. Make sure to use all four numbers.

How many people in this data are males?

How many people in this data are males that intend to make an online purchase?

How many people are females that do not intend to make an online purchase?

Find the probability that a person chosen at random is a male.

Express your answer as a percent (one place past the decimal, use the % sign) or as a decimal proportion (three places past the decimal).

Find the probability that a person chosen at random is a female and intends to buy.

Express your answer as a percent (one place past the decimal, use the % sign) or as a decimal proportion (three places past the decimal).

Find the probability that a person chosen at random is a male and does not intend to buy.

Express your answer as a percent (one place past the decimal, use the % sign)

or

as a decimal proportion (three places past the decimal).

Find the probability that a person chosen at random intends to buy given that they are a female.

Express your answer as a percent (one place past the decimal, use the % sign)

or

as a decimal proportion (three places past the decimal).

Find the probability that a person chosen at random is a male given that they intend to buy online.

Express your answer as a percent (one place past the decimal, use the % sign)

or

as a decimal proportion (three places past the decimal).

Match the following statements with the correct probability notation.

A swim coach has 7 swimmers that he is teaching to be part of a 4-person relay team.

As the coach puts the swimmers into groups of 4 just to practice the relay, would this be a permutation or a combination?

Why?

A swim coach has 7 swimmers that he will enter to be part of a 4-person relay competition. He will use strategy to line them up, such as the fastest two swimmers are the lead and the anchor positions.

As the coach selects the swimmers to create his relay team, would this be a permutation or a combination?

Why?

New research (in 2023) has produced data that shows the distribution of M&M plain candy colors are: 20% red, 24% blue, 13% orange, 18% yellow and 7% brown. The remaining candies are green.

If you pick an M&M at random, what is the probability that it is green?

New research (in 2023) has produced data that shows the distribution of M&M plain candy colors are: 20% red, 24% blue, 13% orange, 18% yellow and 7% brown. The remaining candies are green.

If you pick an M&M at random, what is the probability that it is not green?

P(not green)= 1 - P(green)

New research (in 2023) has produced data that shows the distribution of M&M plain candy colors are: 20% red, 24% blue, 13% orange, 18% yellow and 7% brown. The remaining candies are green.

If you pick an M&M at random, what is the probability that it is pink or red?

P(pink or red)=

New research (in 2023) has produced data that shows the distribution of M&M plain candy colors are: 20% red, 24% blue, 13% orange, 18% yellow and 7% brown. The remaining candies are green.

If you pick three M&M’s (from a very very large bowl, 1000's, so they are independent).

What is the probability that they are all green?

P(green, green, green)=

Round to three or four places past the decimal.

New research (in 2023) has produced data that shows the distribution of M&M plain candy colors are: 20% red, 24% blue, 13% orange, 18% yellow and 7% brown. The remaining candies are green.

If you pick three M&M's, what is the probability that none are yellow?

Hints: P(not yellow) = 1 - P(yellow)

P(not yellow, not yellow, not yellow)=

Round to three or four places past the decimal.

New research (in 2023) has produced data that shows the distribution of M&M plain candy colors are: 20% red, 24% blue, 13% orange, 18% yellow and 7% brown. The remaining candies are green.

If you select three M&M's what is the probability at least one is yellow?

Remember:

'at least one' reminds us to use 1- the complement

P(at least one of the three is yellow) =1 - P(not yellow, not yellow, not yellow)=

New research (in 2023) has produced data that shows the distribution of M&M plain candy colors are: 20% red, 24% blue, 13% orange, 18% yellow and 7% brown. The remaining candies are green.

If you pick three M&M's what is the probability that the third M&M is the first one that is red?

Hint: P(not red, not red, red)=

1. A county legislature consists of 13 elected representatives, 6 Democrats and 7 Republicans. They’re setting up a 4-person committee to study a proposal to build a new library.

First: how many different committees can be formed from the group of 13 representatives:

1 a. # ways to have a 4 person committee with only 4 Republicans:

1 a. P(only 4 Republicans)

Round to three places past the decimal.

1. c. # ways to have a 4 person committee with only Democrats:

1. c. P(only 4 Democrats):

Round to three decimal places.

1.b. # ways to have 2 Dem and 2 Rep:

This is similar to the Jr/Sr Example problem in our notes or the Playlist problem from the application.

1.b. P( 2 Dem and 2 Rep):

This is similar to the Jr/Sr Example problem in our notes or the Playlist problem from the application.

Round to 3 places.

1.d. # ways to have 3 Dem and 1 Rep on the committee:

1.d. P(3 Dem and 1 Rep on the committee):

Round to three places.

2. a. # combinations of 6 DVD's from the group of 15.

2.b.

P(Only Dramas)

Round to three places past the decimal point.

2.c.

P(3 of comedies & 3 of dramas)

Round to three places past the decimal point.

2.d.

P(3 animated & 3 other)

Round to three places past the decimal point.

3. a. Percent of students with a fever, written as a decimal.

One decimal place answer.

3. b. P(Fever AND sore throat)

Two decimal place answer.

4. a.

On the DHS Varsity baseball team, 5 players are sophomores, 11 are juniors, and 10 are seniors. The team selects 4 honorary co-captains by drawing names from a hat.

How many total combinations of 4 co-captains are possible?

4. b.

On the DHS Varsity baseball team, 5 players are sophomores, 11 are juniors, and 10 are seniors. The team selects 4 honorary co-captains by drawing names from a hat.

How many combinations of 2 Sophomores and 2 Seniors for co-captains are possible?

4. c.

On the DHS Varsity baseball team, 5 players are sophomores, 11 are juniors, and 10 are seniors. The team selects 4 honorary co-captains by drawing names from a hat.

P(2 Sophomore and 2 Senior co-captains)=

Round to 2 or four places.

4.d.

# of 4 co-captain groups that are only Sophomores:

4.d.

# of 4 co-captain groups that are only Juniors:

4.d.

# of 4 co-captain groups that are only Seniors:

4.d.

Total # of 4 co-captain groups that are all the same grade (Soph or Jr or Sr):

4.d.

P(4 co-captain groups that are all the same grade (Soph or Jr or Sr))

Round to three places.

5. a.

The DHS PTSA Social committee has 5 students and 3 teachers.

Find the probability that a 3-person subcommittee from this group includes only students:

Round to three places.

5. b.

The DHS PTSA Social committee has 5 students and 3 teachers.

Find the probability that a 3-person subcommittee from this group includes two students and only one teacher:

Round to three places.

5. d.

The DHS PTSA Social committee has 5 students and 3 teachers.

Find the probability that a 3-person subcommittee from this group includes only teachers (this means no students).

P(no students)=

Round to three places.

5. c.

The DHS PTSA Social committee has 5 students and 3 teachers.

Find the probability that a 3-person subcommittee from this group includes at least one student. See notes 4.6

P(at least one student)= 1-P(no students)

Round to three places.