Compound Probability of Independent Events

The probabilities of simple events can be combined, or compounded, to find the probability of two or more events happening. When outcomes of these events don't depend on each other, the events are considered independent. This lecture series presents examples of calculating compound probabilities of independent events using diagrams. Watch the videos and complete the interactive exercises.

Practice

Sample spaces for compound events - Questions

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}