7.4.0: Exercises

In the following exercises, you are rolling a special 6-sided die that has both a colored letter and a colored number on each face. The faces are labeled with: a red 1 and a blue A, a red 1 and a green A, an orange 1 and a green B, an orange 2 and a red C, a purple 3 and a brown D, an orange 4 and a blue E. You will roll the die once and take note of something about the face that is showing. Identify the sample space:

Exercise \(\PageIndex{1}\)

You note the number.

Exercise \(\PageIndex{2}\)

You note the letter.

Exercise \(\PageIndex{3}\)

You note the color of the number.

Exercise \(\PageIndex{4}\)

You note the color of the letter.

Exercise \(\PageIndex{5}\)

You note the number and letter.

Exercise \(\PageIndex{6}\)

You note the number and its color.

Exercise \(\PageIndex{7}\)

You note the letter and its color.

In Example 7.13, we used a table to identify the possible genetic result when two pea plants are bred; offspring plants get one of the two genes from each parent. Use tables to identify the sample space of offspring for the parents listed in the following exercises:

Exercise \(\PageIndex{8}\)

GG and gg

Exercise \(\PageIndex{9}\)

GG and Gg

Exercise \(\PageIndex{10}\)

Gg and Gg

You’re visiting a pasta bar, where you have your choice of pasta types (cavatappi, ziti, or penne) and sauce (marinara, alfredo, or pesto).

Exercise \(\PageIndex{11}\)

Make a table that shows the sample space for your choices.

Exercise \(\PageIndex{12}\)

Write out the sample space for the pasta bar.

You have a new art print that you’d like to get framed. You have 3 good choices for the material of the frame: oak, maple, and cherry. You’ll also choose a framing mat, for which there are 4 possible colors that will work with your print: plum, lilac, periwinkle, and violet.

Exercise \(\PageIndex{13}\)

Make a table that shows the sample space for your choices.

Exercise \(\PageIndex{14}\)

Write out the sample space for the framing choices.

You are shopping for a new laptop. The brand you’re considering offers laptops with screen sizes 11”, 13”, 14”, 15”, and 17”. It also offers five memory choices: 4GB, 8GB, 12GB, 16GB, and 32GB.

Exercise \(\PageIndex{15}\)

Make a table that shows the sample space for your choices.

Exercise \(\PageIndex{16}\)

Write out the sample space for the laptop choices.

For the following exercises, decide whether the described two-stage experiments have independent or dependent stages.

Exercise \(\PageIndex{17}\)

Siobhan and Tristan are trying to decide where they will have dinner. Siobhan wants to go to Antoine’s, Burger Hut, or the Chowder Palace. Tristan prefers Burger Hut, Chowder Palace, or Duck Duck Taco. They will flip a coin to decide who gets to choose, then that person selects a restaurant from their list.

Exercise \(\PageIndex{18}\)

On the TV game show The Price Is Right, contestants play games to try to win prizes. One of these games is called “Let ‘Em Roll.” In this game, players roll five 6-sided dice. These dice each have 3 faces labeled with a car; the other 3 faces are labeled with prize money amounts (one each of $500, $1,000, and $1,500). Players get to roll all 5 dice, and then have the opportunity to win additional rolls. If all 5 dice show a car, the contestant wins a new car. If not, the contestant can use any additional rolls to reroll the dice with prize money showing to try to win the car (or, they can take the total amount of money showing on the dice and end the game). Josh is playing this game, and he has 2 rolls total (these are the two stages of the experiment; the number of cars showing on the dice will be the reported outcome of each stage).

Exercise \(\PageIndex{19}\)

In the game Rock, Paper, Scissors, each of 2 players secretly chooses 1 of the 3 title objects. The players reveal their choices simultaneously using hand signals. If the players choose the same object, the game is a tie; if they choose different objects, the winner is determined by the following rules: rock beats scissors, scissors beats paper, paper beats rock. Jim and Eva are gearing up to play the game. The two stages of the experiment are Jim’s and Eva’s choices.

Exercise \(\PageIndex{20}\)

Paul is at the racetrack and is about to place a daily double bet, where he will try to predict the winner of 2 consecutive races. The stages of the experiment are the two races.

Exercise \(\PageIndex{21}\)

Mishka is looking for a song to play on a jukebox. The machine requires the user to choose an artist first, then choose a song from among that artist’s songs. The stages of the experiment are choosing the artist and choosing the song.

John is playing a game that involves flipping a coin and rolling dice. The coin flip happens first. If the outcome is heads, the player rolls a 4-sided die. If the outcome is tails, the player rolls a 6-sided die.

Exercise \(\PageIndex{22}\)

Create a tree diagram to display the possible outcomes of this game.

Exercise \(\PageIndex{23}\)

Give the sample space for the game.

In the casino game roulette, a wheel with colored and numbered pockets is spun. At the same time, a marble is spun in the opposite direction in such a way that after a minute or so the marble drops into one of the pockets. Players try to guess the color (red, black, or green) or the number that will appear.

Exercise \(\PageIndex{24}\)

Draw a tree diagram that shows the possible color outcomes for 3 spins of the wheel.

Exercise \(\PageIndex{25}\)

Give the sample space for the three-stage experiment.

Exercise \(\PageIndex{26}\)

Siobhan and Tristan are trying to decide where they will have dinner. Siobhan wants to go to Antoine’s, Burger Hut, or the Chowder Palace. Tristan prefers Burger Hut, Chowder Palace, or Duck Duck Taco. They will flip a coin to decide who gets to choose, then that person selects a restaurant from their list. Use an appropriate method to identify the sample space of possible outcomes, which include the person who chooses and the restaurant.

Exercise \(\PageIndex{27}\)

On the TV game show The Price Is Right, contestants play games to try to win prizes. One of these games is called “Let ‘Em Roll.” In this game, players roll five 6-sided dice. These dice each have 3 faces labeled with a car; the other 3 faces are labeled with prize money amounts (one each of $500, $1000, and $1500). Players get to roll all 5 dice, then have the opportunity to win additional rolls. If all 5 dice show a car, the contestant wins a new car. If not, the contestant can use any additional rolls to reroll the dice with prize money showing to try to win the car (or, they can take the total amount of money showing on the dice and end the game). Kathleen is playing this game, and she has 3 rolls to try to win the car. On her first roll, 3 of the dice showed cars. Use an appropriate method to find the sample space of the number of cars showing after each of the following rolls. Give those outcomes as ordered pairs: (number of cars after the second roll, number of cars after the third roll).

Exercise \(\PageIndex{28}\)

In the game Rock, Paper, Scissors, each of 2 players chooses 1 of the 3 title objects. The players reveal their choices simultaneously using hand signals. Jim and Eva are gearing up to play the game. List the sample space of all the possible outcomes of the first round of their game as ordered pairs of the form (Jim’s choice, Eva’s choice).

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