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A mathematics teacher provides the x- and y- coordinates of 10 points
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07 May 2019, 09:42
07 May 2019, 09:42
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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
A. 1/9
B. 1/5
C. 2/3
D. 4/5
E. 8/9
A mathematics teacher provides the x- and y- coordinates of 10 points
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07 May 2019, 22:12
07 May 2019, 22:12
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mangamma wrote:
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
A. 1/9
B. 1/5
C. 2/3
D. 4/5
E. 8/9
When you look at the coordinates, you should see that y has only 2 values 4 and 5..
So, (0.5,4),(1,4),(2,4),(3,4) are on one line, and other 6 (3,5),(4,5),(5,5),(6,5),(6.5,5) and (7, 5) on other line..
Also both lines are parallel.
We can form a triangle if 2 points are from one line and the third point is on the second line..
so two ways..
1) 2 points on line where y=4....4C2*6C1=36
2) 2 points on line where y=6....6C2*4C1=60
Total 36+60=96
Total ways of choosing 3 points from 10 points = 10C3 = \(\frac{10*9*8}{3*2}=120\)
Thus, probability is \(\frac{96}{120}=\frac{4}{5}\)
D
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Re: A mathematics teacher provides the x- and y- coordinates of 10 points
[#permalink]
08 May 2019, 00:10
08 May 2019, 00:10
mangamma wrote:
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
A. 1/9
B. 1/5
C. 2/3
D. 4/5
E. 8/9
total point 10
∆ we need 3 points ; 10c3 = 120
y coordiante 4 & 5 are common
at 4 ; 4 points and 5 ; 6 points
so ∆ can be made ; 4c2*6c1+6c2*4c1 = 96
96/120 ; 4/5
IMO D
Re: A mathematics teacher provides the x- and y- coordinates of 10 points
[#permalink]
09 Aug 2020, 08:24
09 Aug 2020, 08:24
3
Kudos
Total ways of not forming the triangle = 4C3 + 6C3 = 24
Total ways of selecting points = 10C3 = 120
Probability of not forming a triangle when 3 points are selected = 24/120 = 1/5
Probability of forming a triangle = 1-1/5 = 4/5
Total ways of selecting points = 10C3 = 120
Probability of not forming a triangle when 3 points are selected = 24/120 = 1/5
Probability of forming a triangle = 1-1/5 = 4/5
Re: A mathematics teacher provides the x- and y- coordinates of 10 points
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28 Mar 2024, 05:29
28 Mar 2024, 05:29
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Re: A mathematics teacher provides the x- and y- coordinates of 10 points [#permalink]
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