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Set T consists of all points (x, y) such that x^2 + y^2 = 1.

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Current Student
Joined: 11 May 2008
Posts: 552
Set T consists of all points (x, y) such that x^2 + y^2 = 1. [#permalink]

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26 Aug 2008, 12:26
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Set T consists of all points (x, y) such that x^2 + y^2 = 1. If point (a, b) is selected from set T at random, what is the probability that b> a + 1 ?

1/4
1/3
1/2
3/5
2/3

ZIS A CLUB PROBLEM!! SO CHEERS!! HIC
Director
Joined: 12 Jul 2008
Posts: 513
Schools: Wharton

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26 Aug 2008, 12:38
arjtryarjtry wrote:
Set T consists of all points (x, y) such that x^2 + y^2 = 1. If point (a, b) is selected from set T at random, what is the probability that b> a + 1 ?

1/4
1/3
1/2
3/5
2/3

1/4

x^2 + y^2 = 1 describes a circle with radius 1 centered at (0,0).

Split the circle into fourths using the coordinate plane's quadrants

a and b are positive
Here, b < a + 1

a is negative and b is positive
Here b > a + 1

a is negative and b is negative
Here b < a+1

a is positive and b is negative
Here b < a + 1
SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York

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26 Aug 2008, 23:05
arjtryarjtry wrote:
Set T consists of all points (x, y) such that x^2 + y^2 = 1. If point (a, b) is selected from set T at random, what is the probability that b> a + 1 ?

1/4
1/3
1/2
3/5
2/3

ZIS A CLUB PROBLEM!! SO CHEERS!! HIC

I got 1/4 too..

I drew the CIRCLE with (0,0) as centre .

y=x+1 -- line cuts the circle in II quadrant (1/4 of the circle)
y>x+1 (b>a+1) --> consitute 1/4 of all points.

what is OA.
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Director
Joined: 03 Sep 2006
Posts: 850

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26 Aug 2008, 23:50
x^2 + y^2 = 1 is the equation of a circle with radius "1".

Probability of the following linear equation to hold true;

y > x+1

See the attached file;

shouldn't the answer be = 1/11??
Attachments

Probability2.PNG [ 22.72 KiB | Viewed 920 times ]

Current Student
Joined: 11 May 2008
Posts: 552

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27 Aug 2008, 01:07
yes... even i got a diagram similar to the one above...
so how is the ans 1/4?
when the area above the line is not 1/4 of area of the circle?
Manager
Joined: 14 Jun 2008
Posts: 162

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27 Aug 2008, 01:16
because we are concerned with only point that are ON the circle, not inside
thereofre only that lie on the black

the points in that quadrant are 1/4 of the total circle
Intern
Joined: 23 Feb 2006
Posts: 5

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27 Aug 2008, 01:51
sset009 wrote:
because we are concerned with only point that are ON the circle, not inside
thereofre only that lie on the black

the points in that quadrant are 1/4 of the total circle

Agree. Remember Set T refers to all points that are on the circumference of the circle and not inside.
Re: GEOMETRIC PROB   [#permalink] 27 Aug 2008, 01:51
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Set T consists of all points (x, y) such that x^2 + y^2 = 1.

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