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ACT Exam  >  ACT Questions  >  In a game, 84 marbles numbered 00 through 83 ... Start Learning for Free
In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?
  • a)
    9/84
  • b)
    74/83
  • c)
    9/83
  • d)
    75/84
  • e)
    10/83
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In a game, 84 marbles numbered 00 through 83 are placed in a box. A pl...
Probability of Winning on the Next Draw:

Given Information:
- There are 84 marbles numbered 00 through 83 in the box.
- The first marble drawn by Dave is numbered 23.

To determine the probability of Dave winning on the next draw, we need to consider the possible outcomes and the total number of outcomes.

Possible Outcomes:
Since the first marble drawn by Dave is numbered 23, the second marble he draws must also have the tens digit of 2. This means the second marble can have any number between 20 and 29.

Total Number of Outcomes:
Out of the 84 marbles in the box, there are 10 marbles with tens digit of 2 (20, 21, 22, 23, 24, 25, 26, 27, 28, 29).

Therefore, the total number of outcomes is 10.

Probability Calculation:
The probability of an event is defined as the number of favorable outcomes divided by the total number of outcomes.

In this case, there is only 1 favorable outcome (the second marble having a tens digit of 2) out of a total of 10 outcomes.

So, the probability of Dave winning on the next draw is 1/10.

However, the question asks for the probability as a fraction in the given answer choices. To convert 1/10 to a fraction with a denominator of 84, we multiply both the numerator and denominator by 8.

(1/10) * (8/8) = 8/80

Now, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 8.

8/80 = 1/10

Final Answer:
The probability that Dave will be a winner on the next draw is 1/10, which is equivalent to 9/90. Therefore, the correct answer is option C) 9/83.
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Community Answer
In a game, 84 marbles numbered 00 through 83 are placed in a box. A pl...
The rules of the game state that a player is a winner if two marbles drawn have the same tens digit. The player has already drawn the marble numbered 23, which has a 2 in the tens digit. In order to win, the player must draw another marble witha2inthe tens digit. The possible winning marbles are 20, 21, 22, 24, 25, 26, 27, 28, and 29. Therefore, the player has nine chances to draw a winning marble. Since he has already drawn one of the 84 marbles and did not put it back, he has nine chances out of 83 to draw a winning marble. The probability is 9/83
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Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will find alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also find questions about a particular section of the passage, or about the entire passage. These questions will be identified either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassageThe Fruit of the VineIt is difficult to imagine a human diet without tomatoes in some form, whether a fresh tomato right off the vine or in a spaghetti sauce over pasta. (1) Having become a staple of the American kitchen, tomatoes are even when out of season and of inferior quality.During the growing season, tomatoes of every variety abound in (2) grocery stores, roadside stands, and even on tables in front of peoples’ homes. With tomatoes so readily available during the growing season, it’s easy to run out of things to do with them. (3) Luckily, there are (4) some plenty ways to use and enjoy this surplus of fresh tomatoes. (5) While all are delicious, recipes for using fresh tomatoes range from a basic tomato salad (sliced tomatoes with oil and vinegar) to complicated saucesrequiring hours to simmer and stew. Many cooks prefer to peel and deseed the (6) tomatoes, while using them in a cooking recipe. Peeling can be (7) easily accomplished by first scoring one end of the tomato with a sharp knife, making a small crosshatch, and then dropping the fruit into boiling water for approximately 30 seconds. (8) Whomever chooses this method should be careful not to splash the hot water when placing the tomato into the pot. After the time is up, the cook can use tongs to remove the tomato from the boiling water and set it (9) aside. Waiting until it is cool enough to handle. The skin can then be easily removed with a sharp kitchen knife, and the tomato’s seeds can be collected in a strainer. This is an important step, (10) as the tomato may still be very hot.Even green tomatoes harvested before the first frost can be ripened indoors or used in a green tomato (11) recipe, greentomatoes placed on a kitchen shelf will ripen nicely in just a short amount of time. Once a tomato is (12) a bright red color, it can be used for cooking or stored for later use. A fresh tomato won’t last long, even in the refrigerator, so it’s best to decide early on which tomatoes should become salsa or sauce and which should be served raw in a salad or sandwich. (13)There is truly only one way to eat a fresh tomato and experience its ultimate taste. Go into a garden, pluck a tomato off the vine, brush off any dirt, and then eat it like an apple. The Italians may have rejected the tomato when it was first introduced to their diets, believing it to be poisonous, but it certainly didn’t take (14) one long to incorporate this delicious fruit into nearly every homemade dish. Biting into a freshly picked, red tomato irrefutably explains why.Q. (2)

Directions:Read the passages and choose the best answer to each question.PassageNATURAL SCIENCE: Michigans Beloved SongbirdSometimes an object in nature is so rare thatit escapes mention in nature books. Such is thecase with the delightful Kirtland’s warbler, a plump,yellow-breasted bird that can be found nesting almost(5) exclusively in the northern half of Michigan’s LowerPeninsula. Although this bird migrates to the Bahamasfor the winter, Michigan is its natural habitat. Unfortu-nately, so few Kirtland’s warblers exist that the speciesis classified endangered. The remaining Kirtland’s(10) warblers now enjoy living in stands of young Jack pineslocated in protected Michigan forests.Interestingly, the Kirtland’s warbler nests onthe ground in the jack pine forests, and not in thetrees themselves. Male warblers generally return to(15) Michigan in May to spend the summer. Females arriveas the males stake out territory and choose a suitablenesting area. At the completion of the long journeyfrom the Bahamas to Michigan, female warblers beginto collect leaves and grass to build their nests. During(20) this process, the female warblers’ mates provides food.Eventually, female Kirtland’s warblers each lay fourto five speckled eggs. The eggs hatch in two to threeweeks, and both the male and female warblers tend tothe chicks. Five weeks after they hatch, the fledglings(25) are prepared to survive on their own.Kirtland’s warblers are extremely fastidious abouttheir habitat. This is probably why these birds havebecome endangered. Kirtland’s warblers insist on liv-ing in expansive areas of Jack pine forest rooted in(30) Grayling sand, which percolates quickly to preventflooding of nests built on or near the ground. Graylingsand also supports the type of plant material that thewarblers prefer for their diet and nest building.If not for ongoing human conservation efforts,(35) this special habitat and this rare bird would probablynot exist today. As the massive 19th-century loggingboom faded in Michigan, natural forest fires increased,fueled by the burgeoning undergrowth. Jack pine num-bers increased dramatically, since the tree depends on(40) regular fires to expose the seeds within its tough cones.The early 1900s, though, saw natural fires suppressedby new forest management policies and, consequently,Jack pine forests quickly diminished. This greatlyreduced the number of nesting areas available for the(45) Kirtland’s warbler.To correct this problem, Jack pine areas are cur-rently managed on a rotating basis. This ensures anappropriate number of nesting sites, which encour-ages warblers to return and reproduce annually. The(50) protected Jack pine forests are also home to the white-tailed deer, the black bear, the Eastern bluebird, theupland sandpiper, and the snowshoe hare. Unfortu-nately, for the Kirtland’s warbler, the brown-headedcowbird is also prevalent in these woods. This brood(55) parasite is well known for its tendency to steal thenests of other birds by replacing the original bird’seggs with its own eggs. When the chicks are hatched,the warblers raise the young cowbirds as their own.This, of course, negatively impacts the population of(60) the Kirtland’s warbler. Studies have shown that when acowbird lays one egg in a warbler’s nest, generally onlyone to three warbler chicks will survive. If two or morecowbird chicks survive in a single warbler nest, noneof the warblers will survive. To combat this dilemma,(65) government programs have been established to trap anderadicate cowbirds that attempt to nest in the warblers’habitat. These efforts have greatly improved the sur-vival and proliferation of the Kirtland’s warbler overthe past few decades.(70) The male Kirtland’s warbler is prized as a song-bird, emitting a persistent, melodic song audible up toa quarter-mile away. For researchers, counting thesesongs becomes important during mating season, sincesaving the warbler from extinction demands an annual(75) census of the population to ensure that conservationmeasures are effective.Debates periodically surface over whether toreplace the robin with the Kirtland’s warbler asMichigan’s state bird. Admirers of the Kirtland’s(80) warbler argue that it is strictly a Michigan bird.Supporters of the robin point out that the Kirtland’swarbler is only present in Michigan for, at most, halfof the year. Perhaps this debate will continue until moreresidents have a chance to see the beautiful and elusive(85) Kirtland’s warbler, which calls Michigan home.Q.According to the passage, which of the following correctly states the relationship of the Jack pine to fire?

Directions:Read the passages and choose the best answer to each question.PassageNATURAL SCIENCE: Michigans Beloved SongbirdSometimes an object in nature is so rare thatit escapes mention in nature books. Such is thecase with the delightful Kirtland’s warbler, a plump,yellow-breasted bird that can be found nesting almost(5) exclusively in the northern half of Michigan’s LowerPeninsula. Although this bird migrates to the Bahamasfor the winter, Michigan is its natural habitat. Unfortu-nately, so few Kirtland’s warblers exist that the speciesis classified endangered. The remaining Kirtland’s(10) warblers now enjoy living in stands of young Jack pineslocated in protected Michigan forests.Interestingly, the Kirtland’s warbler nests onthe ground in the jack pine forests, and not in thetrees themselves. Male warblers generally return to(15) Michigan in May to spend the summer. Females arriveas the males stake out territory and choose a suitablenesting area. At the completion of the long journeyfrom the Bahamas to Michigan, female warblers beginto collect leaves and grass to build their nests. During(20) this process, the female warblers’ mates provides food.Eventually, female Kirtland’s warblers each lay fourto five speckled eggs. The eggs hatch in two to threeweeks, and both the male and female warblers tend tothe chicks. Five weeks after they hatch, the fledglings(25) are prepared to survive on their own.Kirtland’s warblers are extremely fastidious abouttheir habitat. This is probably why these birds havebecome endangered. Kirtland’s warblers insist on liv-ing in expansive areas of Jack pine forest rooted in(30) Grayling sand, which percolates quickly to preventflooding of nests built on or near the ground. Graylingsand also supports the type of plant material that thewarblers prefer for their diet and nest building.If not for ongoing human conservation efforts,(35) this special habitat and this rare bird would probablynot exist today. As the massive 19th-century loggingboom faded in Michigan, natural forest fires increased,fueled by the burgeoning undergrowth. Jack pine num-bers increased dramatically, since the tree depends on(40) regular fires to expose the seeds within its tough cones.The early 1900s, though, saw natural fires suppressedby new forest management policies and, consequently,Jack pine forests quickly diminished. This greatlyreduced the number of nesting areas available for the(45) Kirtland’s warbler.To correct this problem, Jack pine areas are cur-rently managed on a rotating basis. This ensures anappropriate number of nesting sites, which encour-ages warblers to return and reproduce annually. The(50) protected Jack pine forests are also home to the white-tailed deer, the black bear, the Eastern bluebird, theupland sandpiper, and the snowshoe hare. Unfortu-nately, for the Kirtland’s warbler, the brown-headedcowbird is also prevalent in these woods. This brood(55) parasite is well known for its tendency to steal thenests of other birds by replacing the original bird’seggs with its own eggs. When the chicks are hatched,the warblers raise the young cowbirds as their own.This, of course, negatively impacts the population of(60) the Kirtland’s warbler. Studies have shown that when acowbird lays one egg in a warbler’s nest, generally onlyone to three warbler chicks will survive. If two or morecowbird chicks survive in a single warbler nest, noneof the warblers will survive. To combat this dilemma,(65) government programs have been established to trap anderadicate cowbirds that attempt to nest in the warblers’habitat. These efforts have greatly improved the sur-vival and proliferation of the Kirtland’s warbler overthe past few decades.(70) The male Kirtland’s warbler is prized as a song-bird, emitting a persistent, melodic song audible up toa quarter-mile away. For researchers, counting thesesongs becomes important during mating season, sincesaving the warbler from extinction demands an annual(75) census of the population to ensure that conservationmeasures are effective.Debates periodically surface over whether toreplace the robin with the Kirtland’s warbler asMichigan’s state bird. Admirers of the Kirtland’s(80) warbler argue that it is strictly a Michigan bird.Supporters of the robin point out that the Kirtland’swarbler is only present in Michigan for, at most, halfof the year. Perhaps this debate will continue until moreresidents have a chance to see the beautiful and elusive(85) Kirtland’s warbler, which calls Michigan home.Q.According to the passage, what is the reason jack pine forests declined in the early 1900s?

Directions:Read the passages and choose the best answer to each question.PassageNATURAL SCIENCE: Michigans Beloved SongbirdSometimes an object in nature is so rare thatit escapes mention in nature books. Such is thecase with the delightful Kirtland’s warbler, a plump,yellow-breasted bird that can be found nesting almost(5) exclusively in the northern half of Michigan’s LowerPeninsula. Although this bird migrates to the Bahamasfor the winter, Michigan is its natural habitat. Unfortu-nately, so few Kirtland’s warblers exist that the speciesis classified endangered. The remaining Kirtland’s(10) warblers now enjoy living in stands of young Jack pineslocated in protected Michigan forests.Interestingly, the Kirtland’s warbler nests onthe ground in the jack pine forests, and not in thetrees themselves. Male warblers generally return to(15) Michigan in May to spend the summer. Females arriveas the males stake out territory and choose a suitablenesting area. At the completion of the long journeyfrom the Bahamas to Michigan, female warblers beginto collect leaves and grass to build their nests. During(20) this process, the female warblers’ mates provides food.Eventually, female Kirtland’s warblers each lay fourto five speckled eggs. The eggs hatch in two to threeweeks, and both the male and female warblers tend tothe chicks. Five weeks after they hatch, the fledglings(25) are prepared to survive on their own.Kirtland’s warblers are extremely fastidious abouttheir habitat. This is probably why these birds havebecome endangered. Kirtland’s warblers insist on liv-ing in expansive areas of Jack pine forest rooted in(30) Grayling sand, which percolates quickly to preventflooding of nests built on or near the ground. Graylingsand also supports the type of plant material that thewarblers prefer for their diet and nest building.If not for ongoing human conservation efforts,(35) this special habitat and this rare bird would probablynot exist today. As the massive 19th-century loggingboom faded in Michigan, natural forest fires increased,fueled by the burgeoning undergrowth. Jack pine num-bers increased dramatically, since the tree depends on(40) regular fires to expose the seeds within its tough cones.The early 1900s, though, saw natural fires suppressedby new forest management policies and, consequently,Jack pine forests quickly diminished. This greatlyreduced the number of nesting areas available for the(45) Kirtland’s warbler.To correct this problem, Jack pine areas are cur-rently managed on a rotating basis. This ensures anappropriate number of nesting sites, which encour-ages warblers to return and reproduce annually. The(50) protected Jack pine forests are also home to the white-tailed deer, the black bear, the Eastern bluebird, theupland sandpiper, and the snowshoe hare. Unfortu-nately, for the Kirtland’s warbler, the brown-headedcowbird is also prevalent in these woods. This brood(55) parasite is well known for its tendency to steal thenests of other birds by replacing the original bird’seggs with its own eggs. When the chicks are hatched,the warblers raise the young cowbirds as their own.This, of course, negatively impacts the population of(60) the Kirtland’s warbler. Studies have shown that when acowbird lays one egg in a warbler’s nest, generally onlyone to three warbler chicks will survive. If two or morecowbird chicks survive in a single warbler nest, noneof the warblers will survive. To combat this dilemma,(65) government programs have been established to trap anderadicate cowbirds that attempt to nest in the warblers’habitat. These efforts have greatly improved the sur-vival and proliferation of the Kirtland’s warbler overthe past few decades.(70) The male Kirtland’s warbler is prized as a song-bird, emitting a persistent, melodic song audible up toa quarter-mile away. For researchers, counting thesesongs becomes important during mating season, sincesaving the warbler from extinction demands an annual(75) census of the population to ensure that conservationmeasures are effective.Debates periodically surface over whether toreplace the robin with the Kirtland’s warbler asMichigan’s state bird. Admirers of the Kirtland’s(80) warbler argue that it is strictly a Michigan bird.Supporters of the robin point out that the Kirtland’swarbler is only present in Michigan for, at most, halfof the year. Perhaps this debate will continue until moreresidents have a chance to see the beautiful and elusive(85) Kirtland’s warbler, which calls Michigan home.Q.What does the passage offer as evidence that Kirtland’s warblers have environmental sensitivities?

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In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer?
Question Description
In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer?.
Solutions for In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT. Download more important topics, notes, lectures and mock test series for ACT Exam by signing up for free.
Here you can find the meaning of In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In a game, 84 marbles numbered 00 through 83 are placed in a box. A player draws 1 marble at random from the box. Without replacing the first marble, the player draws a second marble at random. If both marbles drawn have the same tens digit (that is, both marbles are numbered between 00 and 09, or 10 and 19, or 20 and 29, etc.), the player is a winner. If the first marble Dave draws is numbered 23, what is the probability that Dave will be a winner on the next draw?a)9/84b)74/83c)9/83d)75/84e)10/83Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice ACT tests.
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