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mathematics
contemporary mathematics

Contemporary Mathematics 1st Edition OpenStax - Solutions

What is the probability that you draw (in order) the letters S-E-E-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 any 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 any order) the letters W-I-S-E?You are drawing Scrabble tiles without replacement from a bag containing the letters A, C, \(E, E, I, N, N, S, S, W\).
What is the probability that you draw (in any order) the letters S-E-E-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 are the odds in favor of rolling a green face?You are rolling a 6 -sided die with 3 orange faces, 2 green faces, and 1 blue face.
What are the odds against rolling a blue face?You are rolling a 6 -sided die with 3 orange faces, 2 green faces, and 1 blue face.
What are the odds in favor of rolling an orange face?You are rolling a 6 -sided die with 3 orange faces, 2 green faces, and 1 blue face.
What are the odds in favor of an event with probability \(\frac{3}{8}\) ?
What are the odds against an event with probability \(\frac{2}{13}\) ?
What is the probability of an event with odds \(9: 4\) against?
What is the probability of an event with odds \(5: 7\) in favor?
You draw an ace or a king.You are about to draw a card at random from a deck containing only these 10 cards: Compute the following probabilities: A, A, A, A, K, K, Q, Q, JV, J.
You draw a ♣ or a ♠ You are about to draw a card at random from a deck containing only these 10 cards: Compute the following probabilities: A, A, A, A, K, K, Q, Q, JV, J.
You draw an ace or a ♥.You are about to draw a card at random from a deck containing only these 10 cards: Compute the following probabilities: A, A, A, A, K, K, Q, Q, JV, J.
You draw a jack or a ♥.You are about to draw a card at random from a deck containing only these 10 cards: Compute the following probabilities: A, A, A, A, K, K, Q, Q, JV, J.
You draw a jack or a ♣ You are about to draw a card at random from a deck containing only these 10 cards: Compute the following probabilities: A, A, A, A, K, K, Q, Q, JV, J.
You draw a king or a ♦.You are about to draw a card at random from a deck containing only these 10 cards: Compute the following probabilities: A, A, A, A, K, K, Q, Q, JV, J.
What is the probability of rolling 2 orange faces?You are rolling two 6-sided dice, each of which has 3 orange faces, 2 green faces, and 1 blue face.
What is the probability of rolling 2 green faces?You are rolling two 6-sided dice, each of which has 3 orange faces, 2 green faces, and 1 blue face.
What is the probability of rolling 1 orange and 1 green face (in any order)?You are rolling two 6-sided dice, each of which has 3 orange faces, 2 green faces, and 1 blue face.
What is the probability of drawing 2 aces?You are about to draw 2 cards at random (without replacement) from a deck containing only these 10 cards: A, A, A, A, K, K, Q, Q, JV, J.
What is the probability of drawing an ace first and a king second?You are about to draw 2 cards at random (without replacement) from a deck containing only these 10 cards: A, A, A, A, K, K, Q, Q, JV, J.
What is the probability of drawing ♠ and ♣ (in any order)?You are about to draw 2 cards at random (without replacement) from a deck containing only these 10 cards: A, A, A, A, K, K, Q, Q, JV, J.
If you roll the die 5 times and note the color showing on each roll, is this a binomial experiment?You are rolling a 6-sided die with 3 orange faces, 2 green faces, and 1 blue face.
If you roll the die 5 times and count the number times you roll a green face, is this a binomial experiment?You are rolling a 6-sided die with 3 orange faces, 2 green faces, and 1 blue face.
If you count how many times you roll the die until you get a blue face, is this a binomial experiment?You are rolling a 6-sided die with 3 orange faces, 2 green faces, and 1 blue face.
\(P(O \leq 7)\)Suppose you're rolling the same colored 6 -sided die 10 times. Let \(O, G\), and \(B\) represent the number of times the die lands with an orange, green, and blue side up, respectively. Find these probabilities (round to 4 decimal places):
\(P(G=5)\)Suppose you're rolling the same colored 6 -sided die 10 times. Let \(O, G\), and \(B\) represent the number of times the die lands with an orange, green, and blue side up, respectively. Find these probabilities (round to 4 decimal places):
\(P(1 \leq B \leq 4)\)Suppose you're rolling the same colored 6 -sided die 10 times. Let \(O, G\), and \(B\) represent the number of times the die lands with an orange, green, and blue side up, respectively. Find these probabilities (round to 4 decimal places):
What is the expected value of the number showing on the die after it's rolled?You are about to roll a 20-sided die with faces labeled as follows: 5 faces have a 1, 6 faces have a 3, 4 faces have a 5, 3 faces have a 7 , and 2 faces have a 9 .
Interpret your answer.You are about to roll a 20-sided die with faces labeled as follows: 5 faces have a 1, 6 faces have a 3, 4 faces have a 5, 3 faces have a 7 , and 2 faces have a 9 .
What is the expected value of this game?You are about to play a game in which you draw 3 ping-pong balls without replacement from a barrel. The barrel contains 6 green balls and 4 red balls. If all 3 of your selections are green, you win \(\$ 5\). If 2 of the 3 are green, you win \(\$ 1\). If 2 or
Interpret your answer.You are about to play a game in which you draw 3 ping-pong balls without replacement from a barrel. The barrel contains 6 green balls and 4 red balls. If all 3 of your selections are green, you win \(\$ 5\). If 2 of the 3 are green, you win \(\$ 1\). If 2 or more of your
Is it advantageous to you to play the game? How do you know?You are about to play a game in which you draw 3 ping-pong balls without replacement from a barrel. The barrel contains 6 green balls and 4 red balls. If all 3 of your selections are green, you win \(\$ 5\). If 2 of the 3 are green, you
What's the expected value of the number of points you win?You roll a standard 6-sided die and win points equal to the square of the number shown.
Interpret your answer.You roll a standard 6-sided die and win points equal to the square of the number shown.
What is the expected value of playing the market?In the classic board game The Game of Life, players have the chance to play the market. A spinner with 10 equally likely spaces is spun to choose a random number. If the result is 3 or less, the player loses \(\$ 25,000\). If the result is 7 or more,
Interpret the answer.In the classic board game The Game of Life, players have the chance to play the market. A spinner with 10 equally likely spaces is spun to choose a random number. If the result is 3 or less, the player loses \(\$ 25,000\). If the result is 7 or more, the player wins \(\$
What is the expected value of this speculation?The Game of Life players also occasionally have the opportunity to speculate. Players choose any 2 of the 10 numbers on the spinner and then give it a spin. If one of their numbers is chosen, they win \(\$ 140,000\); if not, they lose \(\$ 10,000\).
Interpret your answer.The Game of Life players also occasionally have the opportunity to speculate. Players choose any 2 of the 10 numbers on the spinner and then give it a spin. If one of their numbers is chosen, they win \(\$ 140,000\); if not, they lose \(\$ 10,000\).
Which is better for The Game of Life players: playing the market or speculating? How do you know?The Game of Life players also occasionally have the opportunity to speculate. Players choose any 2 of the 10 numbers on the spinner and then give it a spin. If one of their numbers is chosen, they win
What is the expected value of a single ticket?A charitable organization is selling raffle tickets as a fundraiser. They intend to sell 5,000 tickets at \(\$ 10\) each. One ticket will be randomly selected to win the grand prize of a new car worth \(\$ 35,000\).
Interpret your answer.A charitable organization is selling raffle tickets as a fundraiser. They intend to sell 5,000 tickets at \(\$ 10\) each. One ticket will be randomly selected to win the grand prize of a new car worth \(\$ 35,000\).
The organization is worried they won't be able to sell all the tickets, so they announce that, in addition to the grand prize, they will offer 10 second prizes of \(\$ 500\) in cash. What is the new expected value of a single ticket?A charitable organization is selling raffle tickets as a
Interpret your answer.A charitable organization is selling raffle tickets as a fundraiser. They intend to sell 5,000 tickets at \(\$ 10\) each. One ticket will be randomly selected to win the grand prize of a new car worth \(\$ 35,000\).
If you draw a single ball, what is the expected number of yellow balls selected?Involve randomly selecting golf balls from a bucket. The bucket contains 4 yellow balls (numbered 1-4) and 6 white balls (numbered 1-6).
Suppose you draw 2 balls with replacement.a. Give a PDF table for the possible outcomes for the number of yellow balls selected.b. What is the expected number of yellow balls selected?Involve randomly selecting golf balls from a bucket. The bucket contains 4 yellow balls (numbered 1-4) and 6 white
Suppose you draw 2 balls without replacement.a. Give a PDF table for the possible outcomes for the number of yellow balls selected.b. What is the expected number of yellow balls selected?Involve randomly selecting golf balls from a bucket. The bucket contains 4 yellow balls (numbered 1-4) and 6
Suppose you draw 3 balls with replacement.a. Give a PDF table for the possible outcomes for the number of yellow balls selected.b. What is the expected number of yellow balls selected?Involve randomly selecting golf balls from a bucket. The bucket contains 4 yellow balls (numbered 1-4) and 6 white
Suppose you draw 3 balls without replacement.a. Give a PDF table for the possible outcomes for the number of yellow balls selected.b. What is the expected number of yellow balls selected?Involve randomly selecting golf balls from a bucket. The bucket contains 4 yellow balls (numbered 1-4) and 6
If you draw a single ball, what is the expected value of the number on the ball?Involve randomly selecting golf balls from a bucket. The bucket contains 4 yellow balls (numbered 1-4) and 6 white balls (numbered 1-6).
Suppose you draw 2 balls with replacement.a. Give a PDF table for the possible outcomes for the sum of the numbers on the selected balls.b. What is the expected sum of the numbers on the balls?Involve randomly selecting golf balls from a bucket. The bucket contains 4 yellow balls (numbered 1-4) and
Suppose you draw 2 balls without replacement.a. Give a PDF table for the possible outcomes for the sum of the numbers on the selected balls.b. What is the expected sum of the numbers on the balls?Involve randomly selecting golf balls from a bucket. The bucket contains 4 yellow balls (numbered 1-4)
If Anita got \(\$ 500\) on her first punch, what's the expected value of her second punch?The following exercise deal with the game "Punch a Bunch," which appears on the TV game show The Price Is Right. In this game, contestants have a chance to punch through up to 4 paper circles on a board;
If Anita got \(\$ 500\) on her first punch, should she throw out her \(\$ 500\) and take the results of her second punch? How do you know?The following exercise deal with the game "Punch a Bunch," which appears on the TV game show The Price Is Right. In this game, contestants have a chance to punch
If Anita got \(\$ 1,000\) on her first punch, what's the expected value of her second punch?The following exercise deal with the game "Punch a Bunch," which appears on the TV game show The Price Is Right. In this game, contestants have a chance to punch through up to 4 paper circles on a board;
If Anita got \(\$ 1,000\) on her first punch, should she throw out her \(\$ 1,000\) and take the results of her second punch? How do you know?The following exercise deal with the game "Punch a Bunch," which appears on the TV game show The Price Is Right. In this game, contestants have a chance to
If Anita got \(\$ 2,500\) on her first punch, what's the expected value of her second punch?The following exercise deal with the game "Punch a Bunch," which appears on the TV game show The Price Is Right. In this game, contestants have a chance to punch through up to 4 paper circles on a board;
If Anita got \(\$ 2,500\) on her first punch, should she throw out her \(\$ 2,500\) and take the results of her second punch? How do you know?The following exercise deal with the game "Punch a Bunch," which appears on the TV game show The Price Is Right. In this game, contestants have a chance to
If a player makes a \(\$ 1\) bet on a single number, they win \(\$ 35\) if that number comes up, but lose \(\$ 1\) if it doesn't. What is the expected value of this bet?The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets
Interpret your answer to the previous question.The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36 , along with a "double zero") and
Suppose a player makes the \(\$ 1\) bet on a single number in 5 consecutive spins. What is the expected value of this series of bets? (use the Binomial Distribution.)The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets
Interpret your answer to the previous question.The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36 , along with a "double zero") and
If a player makes a \(\$ 10\) bet on first dozen, they win \(\$ 20\) if one of the numbers \(1-12\) comes up but lose \(\$ 10\) otherwise. What is the expected value of this bet?The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38
Interpret your answer to the previous question.The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36 , along with a "double zero") and
Suppose a player makes the \(\$ 10\) bet on first dozen in 4 consecutive spins. What is the expected value of that series of bets?The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each
Interpret your answer to the previous question.The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36 , along with a "double zero") and
If a player makes a \(\$ 10\) basket bet, they win \(\$ 60\) if \(0,00,1,2\), or 3 come up but lose \(\$ 10\) otherwise. What is the expected value of this bet?The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the
Interpret your answer to previous question.The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36 , along with a "double zero") and a
Which is better for the player: a \(\$ 10\) first dozen bet or a \(\$ 10\) basket bet? How do you know?The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each
What is the probability of rolling a 1 or a 2 ?We are considering a special 6-sided die, with faces that are labeled with a number and a letter: \(1 A, 1 B, 2 A, 2 C, 4 A\), and \(4 E\). You are about to roll this die once.
What is the probability of rolling a 4 or a \(B\) ?We are considering a special 6-sided die, with faces that are labeled with a number and a letter: \(1 A, 1 B, 2 A, 2 C, 4 A\), and \(4 E\). You are about to roll this die once.
What is the probability of rolling an even number or a consonant?We are considering a special 6-sided die, with faces that are labeled with a number and a letter: \(1 A, 1 B, 2 A, 2 C, 4 A\), and \(4 E\). You are about to roll this die once.
What is the probability of rolling a 2 or an \(E\) ?We are considering a special 6-sided die, with faces that are labeled with a number and a letter: \(1 A, 1 B, 2 A, 2 C, 4 A\), and \(4 E\). You are about to roll this die once.
What is the probability of rolling an odd number or a vowel?We are considering a special 6-sided die, with faces that are labeled with a number and a letter: \(1 A, 1 B, 2 A, 2 C, 4 A\), and \(4 E\). You are about to roll this die once.
What is the probability of rolling an odd number or a consonant?We are considering a special 6-sided die, with faces that are labeled with a number and a letter: \(1 A, 1 B, 2 A, 2 C, 4 A\), and \(4 E\). You are about to roll this die once.
What is the probability that you draw a ♥ or ♠ ?You are drawing a single card from a standard 52-card deck.
What is the probability that you draw a ♥ or a 5 ?You are drawing a single card from a standard 52-card deck.
What is the probability that you draw a 2 or a 3 ?You are drawing a single card from a standard 52-card deck.
What is the probability that you draw a card with an even number on it?You are drawing a single card from a standard 52-card deck.
What is the probability that you draw a card with an even number on it or a ♣ ?You are drawing a single card from a standard 52-card deck.
What is the probability that you draw an ace or a king?You are drawing a single card from a standard 52-card deck.
What is the probability that you draw a face card (king, queen, or jack)?You are drawing a single card from a standard 52-card deck.
What is the probability that you draw a face card or a ♣?You are drawing a single card from a standard 52-card deck.
What is the probability that a randomly selected student is a first-year or sophomore?Use the table provided here, which breaks down the enrollment at a certain liberal arts college by class year and area of study: Class Year First-Year Sophomore Junior Senior Totals Area Of Study Arts 138 121 148
What is the probability that a randomly selected student is a junior or an arts major?Use the table provided here, which breaks down the enrollment at a certain liberal arts college by class year and area of study: Class Year First-Year Sophomore Junior Senior Totals Area Of Study Arts 138 121 148
What is the probability that a randomly selected student is majoring in the social sciences or the natural sciences/mathematics?Use the table provided here, which breaks down the enrollment at a certain liberal arts college by class year and area of study: Class Year First-Year Sophomore Junior
What is the probability that a randomly selected student is a social science major or a sophomore?Use the table provided here, which breaks down the enrollment at a certain liberal arts college by class year and area of study: Class Year First-Year Sophomore Junior Senior Totals Area Of Study Arts
What is the probability that a randomly selected student is a senior or is a humanities major?Use the table provided here, which breaks down the enrollment at a certain liberal arts college by class year and area of study: Class Year First-Year Sophomore Junior Senior Totals Area Of Study Arts 138
What is the probability that a randomly selected student is majoring in the arts or humanities?Use the table provided here, which breaks down the enrollment at a certain liberal arts college by class year and area of study: Class Year First-Year Sophomore Junior Senior Totals Area Of Study Arts 138
First dozen (wins if any of the numbers 1-12 come up) or second dozen (wins on 13-24)The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a double
Red (wins on any of the 18 red numbers) or black (wins on any of the 18 black numbers)The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a
Even (wins on any even number 2-36; 0 and 00 both lose this bet) or red The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a double zero) and a
Middle column (the numbers \(2,5,8,11, \ldots, 35\) ) or black The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a double zero) and a color ( 0
Middle column or red The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a double zero) and a color ( 0 and 00 are both green; the other 36
Right column (the numbers \(3,6,9, \ldots, 36\) ) or black The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a double zero) and a color ( 0 and
Right column or red The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a double zero) and a color ( 0 and 00 are both green; the other 36
Odd or black The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a double zero) and a color ( 0 and 00 are both green; the other 36 numbers are
Even or black The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a double zero) and a color ( 0 and 00 are both green; the other 36 numbers are
The street bet (a bet on 3 numbers that make up a row on the table) on \(1,2,3\) or odd The casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a

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