If point (x, y) is selected at random from a square region that has vertex (0, 0), (2, 0), (0, 2), and (2, 2), what is the probability that y-x>1?
(A) 1/8
(B) 3/8
(C) 1/4
(D) 5/8
(E) 3/4
a good questions
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- AleksandrM
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Is it C?
Probability of y > x + 1
0 > 0 + 1 not true
0 > 2 + 1 not true
2 > 0 + 1 true
2 > 2 + 1 not true
1 out of 4 or 1/4.
Probability of y > x + 1
0 > 0 + 1 not true
0 > 2 + 1 not true
2 > 0 + 1 true
2 > 2 + 1 not true
1 out of 4 or 1/4.
- AleksandrM
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You bring up a good point ksh, I might have gone for the easy (trap) answer choice.
Hope someone else could shed some light on this one.
Hope someone else could shed some light on this one.
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Hi all,
Well, y=x+1 is a line. So y>x+1 defines a region above that line.
If you draw the square region and the line you gonna see that the line intersects the Y axis in y=1 and the square top line in the point (1,2) forming a triangle of side 1.
So the probability is the area of the triangle divided by the area of the square.
Area of the triangle = 1/2
Area of the square = 4
So probability is (1/2)/4 = 1/8, chose A.
Well, y=x+1 is a line. So y>x+1 defines a region above that line.
If you draw the square region and the line you gonna see that the line intersects the Y axis in y=1 and the square top line in the point (1,2) forming a triangle of side 1.
So the probability is the area of the triangle divided by the area of the square.
Area of the triangle = 1/2
Area of the square = 4
So probability is (1/2)/4 = 1/8, chose A.
Last edited by atlantic on Wed Jun 25, 2008 10:01 am, edited 1 time in total.
- AleksandrM
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is 1/8 the answer
if that is the answer the solution is
y-x =1 is the line which passes through points (1,2) and (0,1) and y-x>1 corresponds to area above this line
the total area of the square is 4
the area of the region above the line y-x=1 is 1/2*1*1 = 1/2
hence the probability is 1/2 divided by the whole area which is 4
hence 1/8
if that is the answer the solution is
y-x =1 is the line which passes through points (1,2) and (0,1) and y-x>1 corresponds to area above this line
the total area of the square is 4
the area of the region above the line y-x=1 is 1/2*1*1 = 1/2
hence the probability is 1/2 divided by the whole area which is 4
hence 1/8