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DIRECTIONS for the question: Solve the following question and mark the best possible option.
Sameer is part of a 14 member cricket squad, which consists of the captain (who is also a batsman), a wicketkeeper, six other batsmen, and six bowlers. Sameer is a batsman but not the captain. For the next match, an 11 member team needs to be chosen from this squad, and the captain and the wicketkeeper are sure to play. The team should have at least five batsmen (including the captain but not including the wicketkeeper) and at least four bowlers.
Q. What is the probability that Sameer will play the next match, assuming that all possible team combinations are equally likely?
- a)5 / 12
- b)2 / 3
- c)3 / 4
- d)10 / 13
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
As the captain and the wicketkeeper are definitely in, there are only two cases here, choosing either four batsmen and five bowlers out of six each or five batsmen and four bowlers out of six each.
Since both the team combinations are equally likely, each of the remaining 12 players in the squad has an equal chance of being selected in the remaining 9 spots in the team.
Therefore the probability of each player is equal, and is 9/12 = ¾.
Therefore the probability of each player is equal, and is 9/12 = ¾.
Most Upvoted Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Analysis:
In order to find the probability that Sameer will play the next match, we need to consider the possible combinations of the team and determine the favorable outcomes for Sameer.
Given:
Total squad members = 14
Captain = 1 (batsman)
Wicketkeeper = 1
Batsmen (excluding captain) = 6
Bowlers = 6
Team Selection Criteria:
- Total members in the playing XI = 11
- Captain and wicketkeeper are sure to play
- At least 5 batsmen (including the captain) should be in the team
- At least 4 bowlers should be in the team
Possible Combinations:
To calculate the probability, we need to determine the total number of favorable outcomes for Sameer and the total number of possible outcomes for the team selection.
Step 1: Determine the number of ways to select batsmen:
Since the captain is also a batsman and must be included, we need to select 4 more batsmen from the remaining 5.
Number of ways to select 4 batsmen from 5 = (5 choose 4) = 5
Step 2: Determine the number of ways to select bowlers:
Since the captain is also a bowler and must be included, we need to select 3 more bowlers from the remaining 5.
Number of ways to select 3 bowlers from 5 = (5 choose 3) = 10
Step 3: Determine the number of ways to select the remaining players:
We have already selected the captain and wicketkeeper, along with 5 batsmen and 4 bowlers. We need to select 1 more player from the remaining 1 batsman and 2 bowlers.
Number of ways to select 1 batsman from 1 = (1 choose 1) = 1
Number of ways to select 2 bowlers from 2 = (2 choose 2) = 1
Total Possible Outcomes:
To calculate the total number of possible outcomes, we need to select 5 batsmen from the 6 available (excluding the captain), and 4 bowlers from the 6 available.
Number of ways to select 5 batsmen from 6 = (6 choose 5) = 6
Number of ways to select 4 bowlers from 6 = (6 choose 4) = 15
Total possible outcomes = Number of ways to select 5 batsmen * Number of ways to select 4 bowlers = 6 * 15 = 90
Favorable Outcome:
The favorable outcome is when Sameer is selected in the team. Since Sameer is a batsman, he can be included in the team in any of the 5 batsmen positions.
Number of ways to include Sameer in the team = 5
Calculation:
Probability = Favorable outcomes / Total outcomes = Number of ways to include Sameer in the team / Total possible outcomes = 5 / 90
Simplifying the fraction, we get 1 / 18.
Therefore, the probability that Sameer will play the next match is 1 / 18.
Final Answer:
Option (d)
In order to find the probability that Sameer will play the next match, we need to consider the possible combinations of the team and determine the favorable outcomes for Sameer.
Given:
Total squad members = 14
Captain = 1 (batsman)
Wicketkeeper = 1
Batsmen (excluding captain) = 6
Bowlers = 6
Team Selection Criteria:
- Total members in the playing XI = 11
- Captain and wicketkeeper are sure to play
- At least 5 batsmen (including the captain) should be in the team
- At least 4 bowlers should be in the team
Possible Combinations:
To calculate the probability, we need to determine the total number of favorable outcomes for Sameer and the total number of possible outcomes for the team selection.
Step 1: Determine the number of ways to select batsmen:
Since the captain is also a batsman and must be included, we need to select 4 more batsmen from the remaining 5.
Number of ways to select 4 batsmen from 5 = (5 choose 4) = 5
Step 2: Determine the number of ways to select bowlers:
Since the captain is also a bowler and must be included, we need to select 3 more bowlers from the remaining 5.
Number of ways to select 3 bowlers from 5 = (5 choose 3) = 10
Step 3: Determine the number of ways to select the remaining players:
We have already selected the captain and wicketkeeper, along with 5 batsmen and 4 bowlers. We need to select 1 more player from the remaining 1 batsman and 2 bowlers.
Number of ways to select 1 batsman from 1 = (1 choose 1) = 1
Number of ways to select 2 bowlers from 2 = (2 choose 2) = 1
Total Possible Outcomes:
To calculate the total number of possible outcomes, we need to select 5 batsmen from the 6 available (excluding the captain), and 4 bowlers from the 6 available.
Number of ways to select 5 batsmen from 6 = (6 choose 5) = 6
Number of ways to select 4 bowlers from 6 = (6 choose 4) = 15
Total possible outcomes = Number of ways to select 5 batsmen * Number of ways to select 4 bowlers = 6 * 15 = 90
Favorable Outcome:
The favorable outcome is when Sameer is selected in the team. Since Sameer is a batsman, he can be included in the team in any of the 5 batsmen positions.
Number of ways to include Sameer in the team = 5
Calculation:
Probability = Favorable outcomes / Total outcomes = Number of ways to include Sameer in the team / Total possible outcomes = 5 / 90
Simplifying the fraction, we get 1 / 18.
Therefore, the probability that Sameer will play the next match is 1 / 18.
Final Answer:
Option (d)
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DIRECTIONSfor the question:Solve the following question and mark the best possible option.Sameer is part of a 14 member cricket squad, which consists of the captain (who is also a batsman), a wicketkeeper, six other batsmen, and six bowlers. Sameer is a batsman but not the captain. For the next match, an 11 member team needs to be chosen from this squad, and the captain and the wicketkeeper are sure to play. The team should have at least five batsmen (including the captain but not including the wicketkeeper) and at least four bowlers.Q. What is the probability that Sameer will play the next match, assuming that all possible team combinations are equally likely?a)5 / 12b)2 / 3c)3 / 4d)10 / 13Correct answer is option 'C'. Can you explain this answer?
Question Description
DIRECTIONSfor the question:Solve the following question and mark the best possible option.Sameer is part of a 14 member cricket squad, which consists of the captain (who is also a batsman), a wicketkeeper, six other batsmen, and six bowlers. Sameer is a batsman but not the captain. For the next match, an 11 member team needs to be chosen from this squad, and the captain and the wicketkeeper are sure to play. The team should have at least five batsmen (including the captain but not including the wicketkeeper) and at least four bowlers.Q. What is the probability that Sameer will play the next match, assuming that all possible team combinations are equally likely?a)5 / 12b)2 / 3c)3 / 4d)10 / 13Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.Sameer is part of a 14 member cricket squad, which consists of the captain (who is also a batsman), a wicketkeeper, six other batsmen, and six bowlers. Sameer is a batsman but not the captain. For the next match, an 11 member team needs to be chosen from this squad, and the captain and the wicketkeeper are sure to play. The team should have at least five batsmen (including the captain but not including the wicketkeeper) and at least four bowlers.Q. What is the probability that Sameer will play the next match, assuming that all possible team combinations are equally likely?a)5 / 12b)2 / 3c)3 / 4d)10 / 13Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.Sameer is part of a 14 member cricket squad, which consists of the captain (who is also a batsman), a wicketkeeper, six other batsmen, and six bowlers. Sameer is a batsman but not the captain. For the next match, an 11 member team needs to be chosen from this squad, and the captain and the wicketkeeper are sure to play. The team should have at least five batsmen (including the captain but not including the wicketkeeper) and at least four bowlers.Q. What is the probability that Sameer will play the next match, assuming that all possible team combinations are equally likely?a)5 / 12b)2 / 3c)3 / 4d)10 / 13Correct answer is option 'C'. Can you explain this answer?.
DIRECTIONSfor the question:Solve the following question and mark the best possible option.Sameer is part of a 14 member cricket squad, which consists of the captain (who is also a batsman), a wicketkeeper, six other batsmen, and six bowlers. Sameer is a batsman but not the captain. For the next match, an 11 member team needs to be chosen from this squad, and the captain and the wicketkeeper are sure to play. The team should have at least five batsmen (including the captain but not including the wicketkeeper) and at least four bowlers.Q. What is the probability that Sameer will play the next match, assuming that all possible team combinations are equally likely?a)5 / 12b)2 / 3c)3 / 4d)10 / 13Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.Sameer is part of a 14 member cricket squad, which consists of the captain (who is also a batsman), a wicketkeeper, six other batsmen, and six bowlers. Sameer is a batsman but not the captain. For the next match, an 11 member team needs to be chosen from this squad, and the captain and the wicketkeeper are sure to play. The team should have at least five batsmen (including the captain but not including the wicketkeeper) and at least four bowlers.Q. What is the probability that Sameer will play the next match, assuming that all possible team combinations are equally likely?a)5 / 12b)2 / 3c)3 / 4d)10 / 13Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.Sameer is part of a 14 member cricket squad, which consists of the captain (who is also a batsman), a wicketkeeper, six other batsmen, and six bowlers. Sameer is a batsman but not the captain. For the next match, an 11 member team needs to be chosen from this squad, and the captain and the wicketkeeper are sure to play. The team should have at least five batsmen (including the captain but not including the wicketkeeper) and at least four bowlers.Q. What is the probability that Sameer will play the next match, assuming that all possible team combinations are equally likely?a)5 / 12b)2 / 3c)3 / 4d)10 / 13Correct answer is option 'C'. Can you explain this answer?.
Solutions for DIRECTIONSfor the question:Solve the following question and mark the best possible option.Sameer is part of a 14 member cricket squad, which consists of the captain (who is also a batsman), a wicketkeeper, six other batsmen, and six bowlers. Sameer is a batsman but not the captain. For the next match, an 11 member team needs to be chosen from this squad, and the captain and the wicketkeeper are sure to play. The team should have at least five batsmen (including the captain but not including the wicketkeeper) and at least four bowlers.Q. What is the probability that Sameer will play the next match, assuming that all possible team combinations are equally likely?a)5 / 12b)2 / 3c)3 / 4d)10 / 13Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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