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Probability - A point from region R

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Probability - A point from region R

by Brent@GMATPrepNow » Wed Jan 14, 2009 4:55 pm
Rectangular region R lies on the coordinate plane and has vertices at (0,0), (0,3), (4,3) and (4,0). If a point in region R is randomly selected, what is the probability that the point’s x-coordinate will be greater than the y-coordinate?
(A) 5/16
(B) 5/8
(C) 7/12
(D) 2/3
(E) 3/4
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Re: Probability - A point from region R

by logitech » Wed Jan 14, 2009 6:03 pm
Brent Hanneson wrote:Rectangular region R lies on the coordinate plane and has vertices at (0,0), (0,3), (4,3) and (4,0). If a point in region R is randomly selected, what is the probability that the point’s x-coordinate will be greater than the y-coordinate?
(A) 5/16
(B) 5/8
(C) 7/12
(D) 2/3
(E) 3/4
I might misinterpret the question.

1/2 is not an option
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by Brent@GMATPrepNow » Wed Jan 14, 2009 6:10 pm
This is a good start, Logitech, but I believe that you are assuming that the x- and y-coordinates must be integers.
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by logitech » Wed Jan 14, 2009 6:25 pm
Brent Hanneson wrote:This is a good start, Logitech, but I believe that you are assuming that the x- and y-coordinates must be integers.
No Brent, I actually dont thats why I also have those GREEN areas. But I am still missing something :roll:
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by Brent@GMATPrepNow » Wed Jan 14, 2009 6:28 pm
logitech wrote:
Brent Hanneson wrote:This is a good start, Logitech, but I believe that you are assuming that the x- and y-coordinates must be integers.
No Brent, I actually dont thats why I also have those GREEN areas. But I am still missing something :roll:
Try drawing a straight line from (0,1) to (4,3)
This will divide the region in the appropriate sections.
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by moshum » Wed Jan 14, 2009 7:31 pm
Brent, shouldn't be the straight line from (0,0) to (3,3) to separate the 2 regions?

Because the "switching" points where the y coordinate is getting bigger than the x coordinate is at (0.5,0.5) ; (1,1) ; (2,2) etc...
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by Brent@GMATPrepNow » Wed Jan 14, 2009 7:56 pm
moshum wrote:Brent, shouldn't be the straight line from (0,0) to (3,3) to separate the 2 regions?

Because the "switching" points where the y coordinate is getting bigger than the x coordinate is at (0.5,0.5) ; (1,1) ; (2,2) etc...
Good point, Moshum. My bad.
Yes, once we've drawn the line from (0,0) to (3,3) one region consists of points where the x-coordinate is greater than the y-coordinate and the other region consists of points where the y-coordinate is greater than the x-coordinate.

The total area is 12.
The region where the x-coordinate is greater than the y-coordinate has an area of 7.5
So, the probability is 7.5/12 = 5/8 (answer choice B)
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by Mr2Bits » Thu Jan 15, 2009 7:24 am
Brent Hanneson wrote:
moshum wrote:Brent, shouldn't be the straight line from (0,0) to (3,3) to separate the 2 regions?

Because the "switching" points where the y coordinate is getting bigger than the x coordinate is at (0.5,0.5) ; (1,1) ; (2,2) etc...
Good point, Moshum. My bad.
Yes, once we've drawn the line from (0,0) to (3,3) one region consists of points where the x-coordinate is greater than the y-coordinate and the other region consists of points where the y-coordinate is greater than the x-coordinate.

The total area is 12.
The region where the x-coordinate is greater than the y-coordinate has an area of 7.5
So, the probability is 7.5/12 = 5/8 (answer choice B)
Can you explain the 7.5? Im getting 1/2. I see where you are talking about not being able to assume positive integers but that would inversely work for Y as well wouldn't it?
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by Brent@GMATPrepNow » Thu Jan 15, 2009 9:34 am
It's probably best to draw it.


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I hope that helps.
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