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

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

26 Aug 2008, 12:26

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

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Re: GEOMETRIC PROB [#permalink]

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

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

Quadrant 2:
a is negative and b is positive
Here b > a + 1

Quadrant 3:
a is negative and b is negative
Here b < a+1

Quadrant 4:
a is positive and b is negative
Here b < a + 1

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Re: GEOMETRIC PROB [#permalink]

26 Aug 2008, 23:05

arjtryarjtry wrote:

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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Re: GEOMETRIC PROB [#permalink]

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??

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Probability2.PNG [ 22.72 KiB | Viewed 503 times ]

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Re: GEOMETRIC PROB [#permalink]

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?

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Re: GEOMETRIC PROB [#permalink]

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

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Re: GEOMETRIC PROB [#permalink]

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

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