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A point (x, y) is randomly picked from inside the rectangle with verti

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Bunuel
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A point (x, y) is randomly picked from inside the rectangle with verti [#permalink] New post   19 Mar 2019, 02:25
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A point (x, y) is randomly picked from inside the rectangle with vertices (0, 0), (4, 0), (4, 1), and (0, 1). What is the probability that x < y ?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 3/4
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A
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A point (x, y) is randomly picked from inside the rectangle with verti [#permalink] New post   19 Mar 2019, 04:35
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Bunuel wrote:
A point (x, y) is randomly picked from inside the rectangle with vertices (0, 0), (4, 0), (4, 1), and (0, 1). What is the probability that x < y ?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 3/4


Step-by-step solution is available in video with a few suggestions and tricks talked about for such specific questions



The screenshot for quick understanding is also attached here.




Answer: Option A
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Re: A point (x, y) is randomly picked from inside the rectangle with verti [#permalink] New post   19 Jul 2021, 23:13
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inside the rectangle with vertices
(0, 0), (4, 0), (4, 1), and (0, 1) area of the rectangle =4
probability that x < y
we have to find the area y=x that is inside y>x
y=x meets the rectangle at (1,1)
area of the triangle enclosed by y>x= 1/2*1*1=1/2
Therefore probabbility =(1/2)/4=1/8
Hence IMO A
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Re: A point (x, y) is randomly picked from inside the rectangle with verti [#permalink] New post   19 Mar 2019, 05:38
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Bunuel wrote:
A point (x, y) is randomly picked from inside the rectangle with vertices (0, 0), (4, 0), (4, 1), and (0, 1). What is the probability that x < y ?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 3/4



total area of the rectangle ; 4*1 = 4 units
and the region where y>x will be in range to 1,1 points forming isosceles triangle area ; 1/2 * 1*1 = 1/2
so 1/2/4 = 1/8
IMO A
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Re: A point (x, y) is randomly picked from inside the rectangle with verti [#permalink] New post   15 May 2021, 14:31
Hey!
Could u please explain if y>x, then why (1,1) is a point? Here y=x.

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Re: A point (x, y) is randomly picked from inside the rectangle with verti [#permalink] New post   15 May 2021, 16:01
adilaahsanprita wrote:
Hey!
Could u please explain if y>x, then why (1,1) is a point? Here y=x.

Posted from my mobile device


We want to calculate the probability of x<y. For that, we draw the line x=y which will intersect the rectangle at (1,1). Now, the portion of rectangle left of line x=y will represent x<y and similarly the portion of the rectangle to the right of line x=y will represent x>y.
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Re: A point (x, y) is randomly picked from inside the rectangle with verti [#permalink] New post   25 Apr 2023, 06:35
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Re: A point (x, y) is randomly picked from inside the rectangle with verti [#permalink]
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