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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
\(\frac{10}{13}\)Find the odds in favor of events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds 5:2 and 3:8 can be
\(\frac{8}{15}\)Find the odds in favor of events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds 5:2 and 3:8 can be
\(\frac{2}{7}\)Find the odds against events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5: 2\) and \(3: 8\) can be
\(\frac{12}{17}\)Find the odds against events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5: 2\) and \(3: 8\) can
\(\frac{8}{9}\)Find the odds against events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5: 2\) and \(3: 8\) can be
\(\frac{3}{8}\)Find the odds against events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5: 2\) and \(3: 8\) can be
\(\frac{9}{25}\)Find the odds against events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5: 2\) and \(3: 8\) can be
\(\frac{6}{7}\)Find the odds against events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5: 2\) and \(3: 8\) can be
\(\frac{10}{13}\)Find the odds against events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5: 2\) and \(3: 8\) can
\(\frac{8}{15}\)Find the odds against events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1 , also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5: 2\) and \(3: 8\) can be
Let \(E\) be the event "draw an ace."a. What is the probability of \(E\) ?b. What are the odds in favor of \(E\) ?c. What are the odds against \(E\) ?You are drawing from a deck containing only these 10 cards: A, A, A, A, K, K, Q, Q, JV, J.
Let \(F\) be the event "draw a \(abla^{\prime}\) ".a. What is the probability of \(F\) ?b. What are the odds in favor of \(F\) ?c. What are the odds against \(F\) ?You are drawing from a deck containing only these 10 cards: A, A, A, A, K, K, Q, Q, JV, J.
Let \(T\) be the event "draw two (without replacement)."a. What is the probability of \(T\) ?b. What are the odds in favor of \(T\) ?c. What are the odds against \(T\) ?You are drawing from a deck containing only these 10 cards: A, A, A, A, K, K, Q, Q, JV, J.
Use a table to identify the sample space of the experiment in which we roll both dice and note the sum of the two numbers that are showing.We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the
What is the probability that we roll a sum less than 8 ?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an equal
What is the probability that we roll a sum larger than 8 ?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an
What is the probability that we roll a sum less than or equal to 2 ?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face
What is the probability that we roll a sum greater than 2 ?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an
What is the probability that we roll an even sum?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an equal
What is the probability that we roll an odd sum?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an equal
Use a table to identify the sample space of the experiment in which we roll both dice and note the two letters that are showing.We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has
What is the probability that no As are showing?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an equal
What is the probability that at least one \(A\) is showing?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an
What is the probability that two As are showing?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an equal
What is the probability that two of the same letter are showing?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has
What is the probability that the letter on the first die comes alphabetically before the letter on the second die?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A,
What is the probability that two vowels are showing?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an equal
What is the probability that two consonants are showing?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face has an equal
What is the probability that one consonant and one vowel are showing?We are considering two special 6 -sided dice. Each face is labeled with a number and a letter: the first die has faces \(1 A, 1 B, 2 A, 2 C, 4 A, 4 E\); the second has faces \(1 A, 1 A, 2 A, 2 B, 3 A, 3 C\). Assume that each face
Carolyn is breeding two pea plants, and notes that 8 of the 25 offspring plants have yellow peas. So, she concludes that there's a \(32 \%\) chance that an offspring of these two plants will have yellow peas.Decide whether the given probability was likely determined theoretically, empirically, or
At the beginning of the semester, Malik estimates there's a \(30 \%\) chance that he'll earn As in all his classes.Decide whether the given probability was likely determined theoretically, empirically, or subjectively.
Abbie is deciding where she will attend college in the fall. Right now, she thinks there's an \(80 \%\) chance she'll attend an in-state school.Decide whether the given probability was likely determined theoretically, empirically, or subjectively.
If you roll three standard 6 -sided dice, the probability that the sum will be 8 is \(\frac{21}{216}\).Decide whether the given probability was likely determined theoretically, empirically, or subjectively.
According to the app he uses to play the game, Jason has won 18 of the last 100 games of solitaire he's played. So, the probability that he wins the next one is about \(18 \%\).Decide whether the given probability was likely determined theoretically, empirically, or subjectively.
Jim and Anne are both in a club with 10 members. If 3 people are chosen at random to form a committee, then the probability that both Jim and Anne are chosen is \(\frac{1}{15}\).Decide whether the given probability was likely determined theoretically, empirically, or subjectively.
Mookie Betts gets a home run in his next plate appearance.Use the following table of the top 15 players by number of plate appearances (PA) in the 2019 Major League Baseball season to assign empirical probabilities to the given events. A plate appearance is a batter's opportunity to try to get a
Xander Bogaerts strikes out in his next plate appearance.Use the following table of the top 15 players by number of plate appearances (PA) in the 2019 Major League Baseball season to assign empirical probabilities to the given events. A plate appearance is a batter's opportunity to try to get a
Jonathan Villar gets a hit in his next plate appearance.Use the following table of the top 15 players by number of plate appearances (PA) in the 2019 Major League Baseball season to assign empirical probabilities to the given events. A plate appearance is a batter's opportunity to try to get a hit.
Rhys Hoskins gets a walk in his next plate appearance.Use the following table of the top 15 players by number of plate appearances (PA) in the 2019 Major League Baseball season to assign empirical probabilities to the given events. A plate appearance is a batter's opportunity to try to get a hit.
José Abreu scores a run in his next plate appearance.Use the following table of the top 15 players by number of plate appearances (PA) in the 2019 Major League Baseball season to assign empirical probabilities to the given events. A plate appearance is a batter's opportunity to try to get a hit.
Eduardo Escobar hits a triple in his next plate appearance.Use the following table of the top 15 players by number of plate appearances (PA) in the 2019 Major League Baseball season to assign empirical probabilities to the given events. A plate appearance is a batter's opportunity to try to get a
Whit Merrifield hits a double in his next plate appearance.Use the following table of the top 15 players by number of plate appearances (PA) in the 2019 Major League Baseball season to assign empirical probabilities to the given events. A plate appearance is a batter's opportunity to try to get a
Ronald Acuna Jr. gets an extra-base hit (double, triple, or home run) in his next plate appearance.Use the following table of the top 15 players by number of plate appearances (PA) in the 2019 Major League Baseball season to assign empirical probabilities to the given events. A plate appearance is
What is the probability that a player (not the dealer) is dealt an initial hand worth 21 points? This can only happen with an ace and a card worth 10 points ( \(10, \mathrm{~J}, \mathrm{Q}\), or K).
What is the probability that the dealer is dealt an initial hand worth 21 points, with an ace showing?
What is the probability that a player is dealt 2 cards worth 10 points each?
What is the probability that a player is dealt an initial hand with an 8 and a 3 ?
What is the probability that a player is dealt an initial hand with two 8 s?
What is the probability that a player is dealt 20 ?
In some versions of the game, a player wins automatically if they draw a hand of 5 cards that doesn't go over 21 points. One way this can happen is if they draw 5 cards, all of which are A, 2,3 , or 4 . What is the probability of drawing 5 cards from that collection?
6 horses In horse racing, a trifecta bet is one where the player tries to predict the top three finishers in order. In the following exercises, find the probability of choosing a winning trifecta bet at random when the field contains the given number of horses.
8 horses In horse racing, a trifecta bet is one where the player tries to predict the top three finishers in order. In the following exercises, find the probability of choosing a winning trifecta bet at random when the field contains the given number of horses.
10 horses In horse racing, a trifecta bet is one where the player tries to predict the top three finishers in order. In the following exercises, find the probability of choosing a winning trifecta bet at random when the field contains the given number of horses.
What is the probability of drawing the letters \(E-A-R\), in order?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing the letters \(E-A-R\), in any order?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing the letters S-E-A-L, in order?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing the letters S-E-A-L, in any order?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing the letters L-A-S-S, in order?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing the letters L-A-S-S, in any order?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing 3 tiles that are all vowels?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing 3 tiles that are all consonants?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing 4 tiles in the pattern vowel-consonant-vowel-consonant, in order?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing 2 vowels and 2 consonants, in any order?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing at least 1 vowel when drawing four tiles?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
What is the probability of drawing at least 1 consonant when drawing four tiles?You are about to draw Scrabble tiles from a bag without replacement; the bag contains the letters A, A, C, E, E, E, L, L, N, O, R, S, S, S, T, X.
All 6 cards are rooms.Involve the board game Clue, which involves a deck of 21 cards: 6 suspects, 6 weapons, and 9 rooms. At the beginning of the game, 1 card of each of the 3 types is secretly removed from the deck (the object of the game is to identify those 3 cards). The remaining 18 cards are
5 cards are suspects (the sixth can be anything).Involve the board game Clue, which involves a deck of 21 cards: 6 suspects, 6 weapons, and 9 rooms. At the beginning of the game, 1 card of each of the 3 types is secretly removed from the deck (the object of the game is to identify those 3 cards).
None of the cards are rooms.Involve the board game Clue, which involves a deck of 21 cards: 6 suspects, 6 weapons, and 9 rooms. At the beginning of the game, 1 card of each of the 3 types is secretly removed from the deck (the object of the game is to identify those 3 cards). The remaining 18 cards
None of the cards are suspects.Involve the board game Clue, which involves a deck of 21 cards: 6 suspects, 6 weapons, and 9 rooms. At the beginning of the game, 1 card of each of the 3 types is secretly removed from the deck (the object of the game is to identify those 3 cards). The remaining 18
3 cards are suspects and 3 are weapons.Involve the board game Clue, which involves a deck of 21 cards: 6 suspects, 6 weapons, and 9 rooms. At the beginning of the game, 1 card of each of the 3 types is secretly removed from the deck (the object of the game is to identify those 3 cards). The
There are 2 cards of each type.Involve the board game Clue, which involves a deck of 21 cards: 6 suspects, 6 weapons, and 9 rooms. At the beginning of the game, 1 card of each of the 3 types is secretly removed from the deck (the object of the game is to identify those 3 cards). The remaining 18
There are 3 rooms, 2 suspects, and 1 weapon.Involve the board game Clue, which involves a deck of 21 cards: 6 suspects, 6 weapons, and 9 rooms. At the beginning of the game, 1 card of each of the 3 types is secretly removed from the deck (the object of the game is to identify those 3 cards). The
There are 4 rooms and 5 suspects.Involve the board game Clue, which involves a deck of 21 cards: 6 suspects, 6 weapons, and 9 rooms. At the beginning of the game, 1 card of each of the 3 types is secretly removed from the deck (the object of the game is to identify those 3 cards). The remaining 18
You're packing for vacation, and you need to pick 5 shirts.Decide whether the situation describes a permutation or a combination.
You and your friends are about to play a game, and you need to decide who will have the first turn, second turn, and so on.Decide whether the situation describes a permutation or a combination.
You are watching your favorite reality show, and you want to know how many possibilities there are for the order of finish for the top three.Decide whether the situation describes a permutation or a combination.
You are going to be working in groups of 4 with your classmates, and you want to know how many possibilities there are for the composition of your group.Decide whether the situation describes a permutation or a combination.
\({ }_{5} C_{3}\)Express your answers as whole numbers.
\({ }_{8} C_{2}\)Express your answers as whole numbers.
\({ }_{8} C_{6}\)Express your answers as whole numbers.
\({ }_{12} C_{3}\)Express your answers as whole numbers.
\({ }_{12} C_{5}\)Express your answers as whole numbers.
\({ }_{14} C_{3}\)Express your answers as whole numbers.
\({ }_{14} C_{10}\)Express your answers as whole numbers.
\({ }_{15} C_{5}\)Express your answers as whole numbers.
\({ }_{15} C_{13}\)Express your answers as whole numbers.
\({ }_{18} C_{3}\)Express your answers as whole numbers.
\({ }_{18} C_{6}\)Express your answers as whole numbers.
\({ }_{20} C_{4}\)Express your answers as whole numbers.
In most variations of the card game poker, a hand consists of 5 cards, where the order doesn't matter. How many different poker hands are there?
A professor starts each class by choosing 3 students to present solutions to homework problems to the class. If there are 41 students in the class, in how many different ways can the professor make those selections?
An election for at-large members of a school board has 7 candidates; 3 will be elected. How many different ways can those 3 seats be filled?
There are 20 contestants on a reality TV show; at the end of the first episode, 10 are eliminated. How many different groups of eliminated contestants are possible?
At a horse race, bettors can place a bet called an exacta box. For this bet, the player chooses 2 horses; if those horses finish first and second (in either order), the player wins. In a race with 12 horses in the field, how many possible exacta box bets are there?
A euchre hand contains 5 cards. How many ways are there to receive a 5 -card hand (where the order in which the cards are received doesn't matter, i.e., \(90, \mathrm{~J}, \mathrm{~K}, 9,10\) is the same as \(9, \mathrm{~J}, 90, \mathrm{~K}, 10 \mathbf{)}\) )?The following exercise are about the
After all 4 players get their hands, the remaining 4 cards are placed face down in the center of the table. How many different groups of 4 cards are there from this deck?The following exercise are about the card game euchre, which uses a partial standard deck of cards: it only has the cards with
Euchre is played with partners. How many ways are there for 2 partners to receive 5 -card hands (where, as above, the order doesn't matter)? Hint: After the first person gets their cards, there are \(52-5=47\) cards left for the second person.The following exercise are about the card game euchre,
How many ways are there to choose the 2 people in the front row?You and 5 of your friends are at an amusement park, and are about to ride a roller coaster. The cars have room for 6 people arranged in 3 rows of 2 , so you and your friends will perfectly fill one car.
Assuming the front row has been selected, how many ways are there to choose the 2 people in the middle row?You and 5 of your friends are at an amusement park, and are about to ride a roller coaster. The cars have room for 6 people arranged in 3 rows of 2 , so you and your friends will perfectly
Assuming the first 2 rows have been selected, how many ways are there to choose the 2 people in the back row?You and 5 of your friends are at an amusement park, and are about to ride a roller coaster. The cars have room for 6 people arranged in 3 rows of 2 , so you and your friends will perfectly
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