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mathematics
contemporary mathematics

Contemporary Mathematics 1st Edition OpenStax - Solutions

If you draw 2 Scrabble tiles with replacement and ignoring order from a bag containing \(\mathrm{E}, \mathrm{E}, \mathrm{L}, \mathrm{S}\), what is the sample space?
If you read that the probability of flipping 10 heads in a row is \(\frac{1}{1024}\), is that probability most likely theoretical, empirical, or subjective?
If someone tells you that there is a \(40 \%\) chance that a Democrat wins the U.S. Presidential election in 2132 , is that probability most likely theoretical, empirical, or subjective?
If your professor says that you have a \(20 \%\) chance of getting an \(A\) in her class because \(20 \%\) of her students historically have earned As, is that probability most likely theoretical, empirical, or subjective?
What is the probability of rolling a negative number?You are about to roll a standard 12-sided die (with faces labeled 1-12).
What is the probability of rolling a number less than 20 ?You are about to roll a standard 12-sided die (with faces labeled 1-12).
What is the probability of rolling an 11 ?You are about to roll a standard 12-sided die (with faces labeled 1-12).
What is the probability of rolling a number less than 7 ?You are about to roll a standard 12-sided die (with faces labeled 1-12).
What is the probability of not rolling an 11 ?You are about to roll a standard 12-sided die (with faces labeled 1-12).
What is the probability of rolling a multiple of 4 ?You are about to roll a standard 12-sided die (with faces labeled 1-12).
Over the last 30 years, it has rained 12 times on May 1 . What empirical probability would you assign to the event "it rains next May 1 "?You are about to roll a standard 12-sided die (with faces labeled 1-12).
If you draw 4 cards without replacement, what is the probability of drawing a 2, 3, 4, and 5 in order?You're drawing cards from a special deck of cards containing 20, 2, 20, 24, 30, 3, 3, 40, 4, 5.
If you draw 4 cards without replacement, what is the probability of drawing a 2, 3, 4, and 5 in any order?You're drawing cards from a special deck of cards containing 20, 2, 20, 24, 30, 3, 3, 40, 4, 5.
If you draw 3 cards without replacement, what is the probability that you draw a ♥ , a ♣, and a ♥, in order?You're drawing cards from a special deck of cards containing 20, 2, 20, 24, 30, 3, 3, 40, 4, 5.
If you draw 3 cards without replacement, what is the probability that you draw 2 ♥ and 1♣ , in any order?You're drawing cards from a special deck of cards containing 20, 2, 20, 24, 30, 3, 3, 40, 4, 5.
If you roll a standard 20 -sided die (with faces numbered 1-20), what are the odds against rolling a number less than 5 ?
If you roll a standard 20 -sided die (with faces numbered 1-20), what are the odds in favor of rolling greater than a \(5 ?\)
If \(P(E)=\frac{4}{7}\), what are the odds in favor of \(E\) ?
If \(P(E)=\frac{5}{17}\), what are the odds against \(E\) ?
What is the probability of drawing a 2 or a 3 ?You're drawing a single card from a special deck of cards containing 20, 2, 20, 20, 30, 34, 3, 40, 4, 5.
What is the probability of drawing a ♣ or a ♠?You're drawing a single card from a special deck of cards containing 20, 2, 20, 20, 30, 34, 3, 40, 4, 5.
What is the probability of drawing a 2 or a ♥?You're drawing a single card from a special deck of cards containing 20, 2, 20, 20, 30, 34, 3, 40, 4, 5.
What is the probability of drawing an even number or a ♣?You're drawing a single card from a special deck of cards containing 20, 2, 20, 20, 30, 34, 3, 40, 4, 5.
If you draw a single card, what is:a. \(P(\) draw a 2\()\)b. \(P(\) draw a \(2 \mid\) draw a ♥)c. \(P(\) draw a \(2 \mid\) draw a ♠)
If you draw a single card, what is:a. \(P(\) draw a ♥)b. P( draw a ♥ \(\mid\) draw a 3\()\)c. \(P(\) draw a ♥ \(\mid\) draw a 2\()\)
\(P\) (first roll is a 3 and second roll is a 3 )You are playing the following game that involves rolling 2 dice, one at a time. First, you roll a standard 6-sided die. If the result is a 4 or less, your second roll uses a standard 4-sided die. If the result of the first roll is a 5 or 6 , your
\(P(\) first roll is a 6 and second roll is a 6\()\)You are playing the following game that involves rolling 2 dice, one at a time. First, you roll a standard 6-sided die. If the result is a 4 or less, your second roll uses a standard 4-sided die. If the result of the first roll is a 5 or 6 , your
\(P(\) second roll is a 6\()\)You are playing the following game that involves rolling 2 dice, one at a time. First, you roll a standard 6-sided die. If the result is a 4 or less, your second roll uses a standard 4-sided die. If the result of the first roll is a 5 or 6 , your second roll uses a
\(P(\) second roll is a 1\()\)You are playing the following game that involves rolling 2 dice, one at a time. First, you roll a standard 6-sided die. If the result is a 4 or less, your second roll uses a standard 4-sided die. If the result of the first roll is a 5 or 6 , your second roll uses a
Draw 5 cards with replacement from a standard deck and count the number of ♠.Decide whether the described experiment is a binomial experiment. If it is, identify the number of trials and the probability of success in each trial. If it isn't, explain why it isn't.
Draw 5 cards without replacement from a standard deck and count the number of ♠.Decide whether the described experiment is a binomial experiment. If it is, identify the number of trials and the probability of success in each trial. If it isn't, explain why it isn't.
Draw cards from a standard deck and count how many cards are chosen before the first ♠ appears.Decide whether the described experiment is a binomial experiment. If it is, identify the number of trials and the probability of success in each trial. If it isn't, explain why it isn't.
Suppose you are going to roll the die 4 times. Give a full PDF table for the number of times a number greater than 16 appears.You are about to roll a standard 20-sided die. Round answers to 4 decimal places.
If you roll the die 10 times, what is the probability that a number between 1 and 5 (inclusive) comes up exactly once?You are about to roll a standard 20-sided die. Round answers to 4 decimal places
If you roll the die 40 times, what is the probability that 20 comes up fewer than 2 times?You are about to roll a standard 20-sided die. Round answers to 4 decimal places
If you roll the die 40 times, what is the probability that 20 comes up 4 or more times?You are about to roll a standard 20-sided die. Round answers to 4 decimal places
If you roll the die 100 times, what is the probability that the number of times the die lands on something less than or equal to 7 is between 30 and 35 (inclusive)?You are about to roll a standard 20-sided die. Round answers to 4 decimal places
If you roll the die 100 times, what is the probability that the number of times the die lands on something less than or equal to 7 is exactly 36 ?You are about to roll a standard 20-sided die. Round answers to 4 decimal places
If you roll the die 100 times, what is the probability that the die lands on 20 between 5 and 8 times, inclusive?You are about to roll a standard 20-sided die. Round answers to 4 decimal places
You are playing a game where you roll a pair of standard 6 -sided dice. You win \(\$ 32\) if you get a sum of 12 , and lose \(\$ 1\) otherwise. What is the expected value of this game?
Interpret your answer.You are about to roll a standard 20-sided die. Round answers to 4 decimal places
What is the expected value of this game?You are playing a game where you roll a standard 12 -sided die 4 times. If you roll 12 four times, you win \(\$ 1,000\). If you roll 12 three times, you win \(\$ 100\). If you roll 12 twice, you win \(\$ 10\). If you roll 12 one time, you don't win or lose
Interpret your answer.You are playing a game where you roll a standard 12 -sided die 4 times. If you roll 12 four times, you win \(\$ 1,000\). If you roll 12 three times, you win \(\$ 100\). If you roll 12 twice, you win \(\$ 10\). If you roll 12 one time, you don't win or lose anything. If you
Which game would be better to play? Why?You are playing a game where you roll a standard 12 -sided die 4 times. If you roll 12 four times, you win \(\$ 1,000\). If you roll 12 three times, you win \(\$ 100\). If you roll 12 twice, you win \(\$ 10\). If you roll 12 one time, you don't win or lose
How many ways are there to draw a vowel and then a consonant from the bag?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
How many ways are there to draw a tile worth an even number of points and then a tile worth an odd number of points from the bag?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1),
How many ways are there to draw 4 tiles from the bag without replacement, if order matters?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
How many ways are there to draw 4 consonants from the bag without replacement, if order matter?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
How many ways are there to draw 4 tiles from the bag with replacement, if order does not matter?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
How many ways are there to draw 4 consonants from the bag with replacement, if order does not matter?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
Give the sample space of the experiment that asks you to draw 2 tiles from the bag with replacement and note their point values, where order doesn't matter. Give the outcomes as ordered pairs.Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as
Give the sample space of the experiment that asks you to draw 2 tiles from the bag with replacement and note their point values, where order doesn't matter. Give the outcomes as ordered pairs.Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as
If you draw a single tile from the bag, what is the probability that it's an E?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
If you draw a single tile from the bag, what is the probability that it's not an A?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
If you draw 3 tiles from the bag without replacement, what is the probability that they spell RED, in order?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
If you draw 3 tiles from the bag without replacement, what is the probability that they spell RED, in any order?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
What are the odds against drawing a vowel?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
Use your answer to question 12 to find the odds against drawing three tiles without replacement and being able to spell RED.Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
If you draw one tile, what is the probability of drawing a J or a K?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
If you draw one tile, what is the probability that it's a vowel or that it's worth more than 4 points?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
Suppose you're about to draw one tile from the bag. Find \(P(\) the letter is \(\mathrm{R})\) and \(P\) (the letter is \(\mathrm{R} \mid\) the point value is 1 ).Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2),
If you draw 2 tiles with replacement, what is the probability of drawing a consonant first and then a vowel?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
If you draw 2 tiles without replacement, what is the probability of drawing a consonant first and then a vowel?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
If you draw 10 tiles with replacement, what is the probability that you draw exactly 3 vowels? Round to 3 decimal places.Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
If you draw 100 tiles with replacement, what is the probability that you draw fewer than 35 vowels? Round to 4 decimal places.Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1),
Find and interpret the expected number of points on the tile, assuming you draw 1 tile from the bag.Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
Find the expected sum of points on 2 tiles, selected without replacement.Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows: \(A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1)\).
If your friend offers you a bet where they pay you \(\$ 10\) if you draw a vowel from the bag, but you owe them \(\$ 5\) if you draw a consonant, should you take it? How do you know?Involve drawing a Scrabble tile from a bag. These tiles are labeled with a letter and a point value, as follows:
A website that lets you build custom belts has 18 different buckles and 30 different straps. How many different belts can be made using those materials?
A chain of chicken restaurants offers a combo that includes your choice of 3 or 5 chicken strips, along with your choice of side dish. If there are 7 side dishes, how many different ways are there to build this combo meal?
When you flip a coin, there are 2 possible outcomes: heads and tails. Let's say you flip a coin 10 times, and after each you write down the result of the flip (H for heads, T for tails). How many different results (strings of 10 characters, where each is either an \(\mathrm{H}\) or a \(\mathrm{T}\)
A T-shirt company allows shoppers to customize their shirts in several ways. There are 5 sizes, 8 shirt colors, 4 designs, and 5 design colors. How many different shirts can be made?
Josephine is trying to build her class schedule for next semester. Because of her work schedule, she has only 4 class periods that can work for her, and she must take 4 classes. If there are 15 classes that she could take during the first period, 18 during the second, 12 during the third, and 8
Compute \(5!\).
Compute \(\frac{10!}{7!3!}\).
Compute \({ }_{12} P_{3}\).
Compute \({ }_{8} P_{4}\).
The standard American edition of the board game Monopoly has a deck of 15 orange Chance cards. In how many different ways could the first 4 Chance cards drawn in a game appear?
Suppose you want to count the number of ways that you can arrange the apps on the home screen on your phone. Should you use permutations or combinations?
Your little brother is packing up for a family vacation, but there's only room for 3 of his toys. If you want to know how many possible groups of toys he can bring, should you use permutations or combinations?
Compute \({ }_{12} C_{10}\).
Compute \({ }_{16} C_{3}\).
You're planning a road trip with some friends. Though you have 6 friends you'd consider bringing along, you only have room for 3 other people in the car. How many different possibilities are there for your road trip squad?
You're packing for a trip, for which you need 3 shirts and 3 skirts. If you have 8 shirts and 5 skirts that would work for the trip, how many different ways are there to pack for the trip?
You flip a coin 6 times and note the number of heads. What is the sample space of this experiment?
You are ordering a combo meal at a restaurant. The meal comes with either 8 or 12 chicken nuggets, and your choice of crinkle fries, curly fries, or onion rings. Create a table to help you identify the sample space containing your combo meal possibilities.
You need one more class to fill out your schedule for next semester. You want to take either History 101 (H), English 220 (E), or Sociology 112 (S). There are two professors teaching the history class: Anderson (A) and Burr (B); one professor teaching the English class: Carter (C); and three people
Identify the sample space from Exercise 18.Data from Exercises 18You are ordering a combo meal at a restaurant. The meal comes with either 8 or 12 chicken nuggets, and your choice of crinkle fries, curly fries, or onion rings. Create a table to help you identify the sample space containing your
Identify the sample space from Exercise 19.Data from Exercises 19You need one more class to fill out your schedule for next semester. You want to take either History 101 (H), English 220 (E), or Sociology 112 (S). There are two professors teaching the history class: Anderson (A) and Burr (B); one
Both come up heads.You have two coins: a nickel and a quarter. You flip them both. Find the probabilities of these events:
The quarter comes up heads.You have two coins: a nickel and a quarter. You flip them both. Find the probabilities of these events:
You get one heads and one tails.You have two coins: a nickel and a quarter. You flip them both. Find the probabilities of these events:
You get three tails.You have two coins: a nickel and a quarter. You flip them both. Find the probabilities of these events:
A poker player has a \(16 \%\) chance of making a hand called a flush on the next card.Decide whether the given probabilities were most likely derived theoretically, empirically, or subjectively.
Your friend Jacob tells you that there's a \(20 \%\) chance he'll get married in the next 5 years.Decide whether the given probabilities were most likely derived theoretically, empirically, or subjectively.
Ashley has a coin that they think might not be fair, so they flip it 100 times and note that the result was heads 58 times. So, Ashley says the probability of flipping heads on that coin is about \(58 \%\).Decide whether the given probabilities were most likely derived theoretically, empirically,
If \(E\) is the event "number of heads is 20 or fewer", describe the event \(E^{\prime}\) using an inequality.If you flip a fair coin 50 times, the probability of getting 20 or fewer heads is about \(10.1 \%\) (a fact we'll learn how to verify later).
Find \(P\left(E^{\prime}\right)\).If you flip a fair coin 50 times, the probability of getting 20 or fewer heads is about \(10.1 \%\) (a fact we'll learn how to verify later).
What is the probability that you draw (in order) the letters W-I-N?You are drawing Scrabble tiles without replacement from a bag containing the letters A, C, \(E, E, I, N, N, S, S, W\).
What is the probability that you draw (in order) the letters W-I-S-E?You are drawing Scrabble tiles without replacement from a bag containing the letters A, C, \(E, E, I, N, N, S, S, W\).

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