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A mathematics teacher provides the x- and y- coordinates of 10 points in a rectangular coordinate system. These points are (0.5, 4), (1, 4), (2, 4), (3, 4), (3, 5), (4, 5), (5, 5), (6, 5), (6.5, 5) and (7, 5). He asks a student to select 3 points at random. What is the probability that the chosen points form a triangle?
  • a)
    1/9
  • b)
    1/5
  • c)
    2/3
  • d)
    4/5
  • e)
    8/9
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A mathematics teacher provides the x- and y- coordinates of 10 points ...
Given:
  • A list of 10 points:
    • (0.5, 4), (1, 4), (2, 4), (3, 4)
      • All these 4 points lie on the line y = 4
    • (3, 5), (4, 5), (5, 5), (6, 5), (6.5, 5), (7, 5)
      • All these 6 points lie on the line y = 5
  • 3 points are chosen at random
To find: P(Chosen points form a triangle)
Approach:
  1. P(Chosen points form a triangle) = 1 – P(Chosen points don’t form a triangle)
    • The only way in which the chosen points will not form a triangle is if all the 3 chosen points are collinear
    • P(Chosen points form a triangle) = 1 – P(Chosen points are Collinear)
  2. All the 3 chosen points will be collinear if either all 3 of them lie on the line y = 4 or on the line y = 5
    • So, P(Chosen points are Collinear) = P(Chosen points lie on y = 4) + P(Chosen points lie on y = 5)
Working Out:
  • Finding P(Chosen points lie on y = 4)
    • There are 4 points that lie on line y = 4
    • So, we have to choose 3 collinear points from these 4 points.
    • Number of ways to choose 3 points out of 4 points =
The total number of given points = 10
  • So, the total number of ways in which 3 points may be chosen =
So, P(Chosen points lie on y = 4) =4/120
Finding P(Chosen points lie on y = 5)
  • There are 6 points that lie on line y = 5
  • So, we have to choose 3 points from these 6 points.
    • Number of ways to choose 3 points out of 6 points =
The total number of given points = 10
  • So, the total number of ways in which 3 points may be chosen =
So, P(Chosen points lie on y = 5) = 20/120
  • Getting to the required Probability
    • So, P(Chosen points are Collinear) = 
P(Chosen points form a triangle) =
Looking at the answer choices, we see that the correct answer is Option D
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A mathematics teacher provides the x- and y- coordinates of 10 points in a rectangular coordinate system. These points are (0.5, 4), (1, 4), (2, 4), (3, 4), (3, 5), (4, 5), (5, 5), (6, 5), (6.5, 5) and (7, 5). He asks a student to select 3 points at random. What is the probability that the chosen points form a triangle?a)1/9b)1/5c)2/3d)4/5e)8/9Correct answer is option 'D'. Can you explain this answer?
Question Description
A mathematics teacher provides the x- and y- coordinates of 10 points in a rectangular coordinate system. These points are (0.5, 4), (1, 4), (2, 4), (3, 4), (3, 5), (4, 5), (5, 5), (6, 5), (6.5, 5) and (7, 5). He asks a student to select 3 points at random. What is the probability that the chosen points form a triangle?a)1/9b)1/5c)2/3d)4/5e)8/9Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A mathematics teacher provides the x- and y- coordinates of 10 points in a rectangular coordinate system. These points are (0.5, 4), (1, 4), (2, 4), (3, 4), (3, 5), (4, 5), (5, 5), (6, 5), (6.5, 5) and (7, 5). He asks a student to select 3 points at random. What is the probability that the chosen points form a triangle?a)1/9b)1/5c)2/3d)4/5e)8/9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mathematics teacher provides the x- and y- coordinates of 10 points in a rectangular coordinate system. These points are (0.5, 4), (1, 4), (2, 4), (3, 4), (3, 5), (4, 5), (5, 5), (6, 5), (6.5, 5) and (7, 5). He asks a student to select 3 points at random. What is the probability that the chosen points form a triangle?a)1/9b)1/5c)2/3d)4/5e)8/9Correct answer is option 'D'. Can you explain this answer?.
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