Compound Probability of Independent Events

1. Harry goes to Hogwarts School of Witchcraft and Wizardry. He can travel to school and back in $3$ different ways: by the Hogwarts Express, a flying car, or the Knight Bus. He's decided to choose his methods of transportation to and from Hogwarts at random this year.

Which of these tables lists all the different ways Harry can get to Hogwarts and back? (Each row represents one outcome.)

Choose all answers that apply:

(A) Table $\mathrm{A}$

(B) Table B

$\begin{aligned}&\text { Table A: }\\&\begin{array}{lr}\hline \text { To Hogwarts } & \text { From Hogwarts } \\\hline \text { Knight Bus } & \text { Knight Bus } \\\hline \text { Knight Bus } & \text { Flying Car } \\\hline \text { Knight Bus } & \text { Hogwarts Express } \\\hline \text { Flying Car } & \text { Knight Bus } \\\hline \text { Flying Car } & \text { Flying Car } \\\hline \text { Flying Car } & \text { Hogwarts Express } \\\hline \text { Hogwarts Express } & \text { Knight Bus } \\\hline \text { Hogwarts Express } & \text { Flying Car } \\\hline \text { Hogwarts Express } & \text { Hogwarts Express } \\\hline \end{array}\end{aligned}$

$\begin{aligned}&\text { Table B: }\\&\begin{array}{lr}\hline  \text { To Hogwarts } & \text { From Hogwarts } \\\hline \text { Knight Bus } & \text { Hogwarts Express } \\\hline \text { Flying Car } & \text { Flying Car } \\\hline \text { Hogwarts Express } & \text { Knight Bus } \\\hline \text { Knight Bus } & \text { Knight Bus } \\\hline \text { Flying Car } & \text { Hogwarts Express } \\\hline \text { Hogwarts Express } & \text { Flying Car } \\\hline \text { Knight Bus } & \text { Flying Car } \\\hline \text { Flying Car } & \text { Knight Bus } \\\hline \text { Hogwarts Express } & \text { Hogwarts Express } \\\hline \end{array}\end{aligned}$

2. You're picking out water balloons. There are $3$ colors and $2$ sizes.

If you randomly pick the color and size, which of these tables lists all possible outcomes? (Each row represents one outcome.)

Choose all answers that apply:

(A) Table A

(B) Table B

$\begin{aligned}&\text { Table A: }\\&\begin{array}{lc}\hline \text { Color } & \text { Size } \\\hline \text { Green } & \text { Large } \\\hline \text { Green } & \text { Small } \\\hline \text { Orange } & \text { Large } \\\hline \text { Orange } & \text { Small } \\\hline \text { Yellow } & \text { Large } \\\hline \text { Yellow } & \text { Small } \\\hline\end{array}\end{aligned}$

$\begin{aligned}&\text { Table B: }\\&\begin{array}{lc}\hline \text { Color } & \text { Size } \\\hline \text { Green } & \text { Large } \\\hline \text { Orange } & \text { Large } \\\hline \text { Yellow } & \text { Large } \\\hline \text { Green } & \text { Small } \\\hline \text { Orange } & \text { Small } \\\hline \text { Yellow } & \text { Small } \\\hline \end{array}\end{aligned}$

3. It's make-your-own-dish night at your favorite pasta restaurant. The restaurant offers $5$ types of pasta and $4$ different sauces. You get to choose one of each.

If you randomly choose the pasta and the sauce, which of these diagrams can be used to find all of the possible outcomes?

Choose all answers that apply:

(A) Diagram A

(B) Diagram B

4. You've decided to take $3$ steps and randomly choose left or right as the direction each time.

Which of these tables lists all possible outcomes of your random walk? (Each row represents one outcome.)

Choose all answers that apply:

(A) Table A

(B) Table B

$\begin{aligned}&\text { Table A: }\\&\begin{array}{lcc}\text { First } & \text { Second } & \text { Third } \\\hline \text { Left } & \text { Left } & \text { Left } \\\hline \text { Left } & \text { Left } & \text { Right } \\\hline \text { Left } & \text { Right } & \text { Left } \\\hline \text { Left } & \text { Right } & \text { Right } \\\hline \text { Right } & \text { Left } & \text { Left } \\\hline \text { Right } & \text { Left } & \text { Right } \\\hline \text { Right } & \text { Right } & \text { Left } \\\hline \text { Right } & \text { Right } & \text { Right } \\\hline \end{array}\end{aligned}$

$\begin{aligned}&\text { Table B: }\\&\begin{array}{lcl}\text { First } & \text { Second } & \text { Third } \\\hline \text { Right } & \text { Right } & \text { Right } \\\hline \text { Left } & \text { Right } & \text { Right } \\\hline \text { Right } & \text { Left } & \text { Right } \\\hline \text { Left } & \text { Left } & \text { Right } \\\hline \text { Right } & \text { Right } & \text { Left } \\\hline \text { Left } & \text { Right } & \text { Left } \\\hline \text { Right } & \text { Left } & \text { Left } \\\hline \text { Left } & \text { Left } & \text { Left } \\\hline \end{array}\end{aligned}$

1. These tables are organized differently, but they both list all $9$ possible outcomes.

2. These tables are organized differently, but they both list all $6$ possible outcomes.

3. Diagram B shows all $20$ possible combinations of one pasta type and one sauce.

4. These tables are organized differently, but they both list all $8$ possible outcomes.

1. Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has 3 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 choices for her trip home.

If Elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?

________

2. If you roll two fair six-sided dice, what is the probability that the sum is $9$ or higher?

________

3. You're at a clothing store that dyes your clothes while you wait. You get to pick from $4$ pieces of clothing (shirt, pants, socks, or hat) and $3$ colors (purple, blue, or orange).

If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?

________

4. If you flip three fair coins, what is the probability that you'll get heads on the first two flips and tails on the last flip?

________

1. The probability that Elizabeth will use a cab once is $4$ out of $9$, or $\frac{4}{9}$.

2. The probability of rolling a $9$ or higher is $\frac{10}{36}$. We can simplify this fraction to $\frac{5}{18}$.

3. The probability of randomly picking an orange hat is $1$ out of $12$, or $\frac{1}{12}$.

4. The probability of getting heads on the first two flips and tails on the last flip is $\frac{1}{8}$.

1. Carlos is almost old enough to go to school! Based on where he lives, there are $6$ elementary schools, $3$ middle schools, and $2$ high schools that he has the option of attending.

How many different education paths are available to Carlos? Assume he will attend only one of each type of school.

__________

2. Bruno is designing his next skateboard. The skateboard store has $2$ types of grip tape, $13$ types of decks, $7$ types of trucks, $4$ types of bearings, and $2$ types of wheels.

How many different skateboards can Bruno create? Assume each skateboard will contain only one type of each component.

__________

3. John always wears a shirt, pants, socks, and shoes. He owns $12$ pairs of socks, $3$ pairs of shoes, $5$ pairs of pants, and $5$ shirts.

How many different outfits can John make?

__________

4. Sebastian is going to choose the color, pattern, font, and image for the design of a sweatshirt for his dance team. There are $10$ colors, $4$ patterns, $12$ fonts, and $9$ images for him to choose from. (The printing company charges a fee to add extra design elements, so he will choose only one of each.)

How many different sweatshirt designs are possible?

__________

1. There are $36$ different education paths available to Carlos.

2. Bruno can create $2184$ different skateboards.

3. John can make $900$ different outfits.

4. There are $4320$ different possible sweatshirt designs.