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Set T consists of all points (x, y) such that x^2 + y^2 = 1. [#permalink ]
26 Aug 2008, 11:26

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

ZIS A CLUB PROBLEM!! SO CHEERS!! HIC

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Re: GEOMETRIC PROB [#permalink ]
26 Aug 2008, 11:38

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, 22:05

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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Re: GEOMETRIC PROB [#permalink ]
26 Aug 2008, 22:50

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 642 times ]

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Re: GEOMETRIC PROB [#permalink ]
27 Aug 2008, 00:07

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, 00:16

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, 00:51

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, 00:51

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