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Consider the collection of points (a, b) in the coordinate plane such that a and b are integers such that – 5 ≤ a ≤ 5 and -5 ≤ b ≤ 5. A point is selected at random from the collection. What is the probability that the selected point is at a distance of atmost 2 units from the origin?
- a)11/100
- b)13/100
- c)11/121
- d)13/121
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Consider the collection of points (a, b) in the coordinate plane such ...
The collection of points can be visualized as a grid of dots, where the x-coordinates are integers from -10 to 10 and the y-coordinates are integers from -10 to 10. However, we need to exclude the points on the x-axis and y-axis, since they do not satisfy the given condition.
To count the number of points in this collection, we can use the principle of inclusion-exclusion. First, we count the total number of points in the grid, which is (21)(21) = 441. Then, we subtract the number of points on the x-axis and y-axis, which is 21 + 21 - 1 = 41 (we subtract 1 because we've counted the origin twice). However, we've now subtracted the point (0,0) twice, so we need to add it back in once. Therefore, the total number of points in the collection is:
441 - 41 + 1 = 401
So there are 401 points in the collection.
To count the number of points in this collection, we can use the principle of inclusion-exclusion. First, we count the total number of points in the grid, which is (21)(21) = 441. Then, we subtract the number of points on the x-axis and y-axis, which is 21 + 21 - 1 = 41 (we subtract 1 because we've counted the origin twice). However, we've now subtracted the point (0,0) twice, so we need to add it back in once. Therefore, the total number of points in the collection is:
441 - 41 + 1 = 401
So there are 401 points in the collection.
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Community Answer
Consider the collection of points (a, b) in the coordinate plane such ...
n(s) = 11 × 11 = 121
p(E) = 13/121
E = {(0, 0), (1, 0), (1, 1), (2, 0), (– 1, 0), (– 2, 0), (0, 2), (0, 1), (0, – 1), (0, – 2), (–1, 1), (1, – 1), (– 1, – 1)}
p(E) = 13/121
E = {(0, 0), (1, 0), (1, 1), (2, 0), (– 1, 0), (– 2, 0), (0, 2), (0, 1), (0, – 1), (0, – 2), (–1, 1), (1, – 1), (– 1, – 1)}
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Consider the collection of points (a, b) in the coordinate plane such that a and b are integers such that – 5 ≤ a ≤ 5 and -5 ≤ b ≤ 5. A point is selected at random from the collection. What is the probability that the selected point is at a distance of atmost 2 units from the origin?a)11/100b)13/100c)11/121d)13/121Correct answer is option 'D'. Can you explain this answer?
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Consider the collection of points (a, b) in the coordinate plane such that a and b are integers such that – 5 ≤ a ≤ 5 and -5 ≤ b ≤ 5. A point is selected at random from the collection. What is the probability that the selected point is at a distance of atmost 2 units from the origin?a)11/100b)13/100c)11/121d)13/121Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Consider the collection of points (a, b) in the coordinate plane such that a and b are integers such that – 5 ≤ a ≤ 5 and -5 ≤ b ≤ 5. A point is selected at random from the collection. What is the probability that the selected point is at a distance of atmost 2 units from the origin?a)11/100b)13/100c)11/121d)13/121Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the collection of points (a, b) in the coordinate plane such that a and b are integers such that – 5 ≤ a ≤ 5 and -5 ≤ b ≤ 5. A point is selected at random from the collection. What is the probability that the selected point is at a distance of atmost 2 units from the origin?a)11/100b)13/100c)11/121d)13/121Correct answer is option 'D'. Can you explain this answer?.
Consider the collection of points (a, b) in the coordinate plane such that a and b are integers such that – 5 ≤ a ≤ 5 and -5 ≤ b ≤ 5. A point is selected at random from the collection. What is the probability that the selected point is at a distance of atmost 2 units from the origin?a)11/100b)13/100c)11/121d)13/121Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Consider the collection of points (a, b) in the coordinate plane such that a and b are integers such that – 5 ≤ a ≤ 5 and -5 ≤ b ≤ 5. A point is selected at random from the collection. What is the probability that the selected point is at a distance of atmost 2 units from the origin?a)11/100b)13/100c)11/121d)13/121Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the collection of points (a, b) in the coordinate plane such that a and b are integers such that – 5 ≤ a ≤ 5 and -5 ≤ b ≤ 5. A point is selected at random from the collection. What is the probability that the selected point is at a distance of atmost 2 units from the origin?a)11/100b)13/100c)11/121d)13/121Correct answer is option 'D'. Can you explain this answer?.
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