IIT JEE , AIEEE Forum - Mathematics , Algebra

ayshwarya

1) A random point A is uniformly distributed in a square of side length 1 unit. Then the probabilities of the following events. The distance from A to fixed side of the square does not exceed x ( x<1 ) is ( ans x )

2) The distance from A to the nearest side does not exceed x[x<1/rt2 ] is

(ans 4x (1-x) )

3) the distance from A to particular side does not exceed its distance to the opposite side (ans 1/2 )

sandeepramesh

1. the probability can be thought of area of rectangle of sides x and side os square divided by are of square = x * 1/1*1 = x :)

sandeepramesh

3. the point can lie in either half of a square (where the square is divided into 2 equal rectangles) so reqd prob = 1/2

akhil_o

2)

draw a square of side length (1-2x) concentric with this one, so that x is distance from each side

so the required point lies outside this square but within second square

area of small square=(1-2x)²
1-P=(1-2x)²/1
=1-4x+4X²
p=4x-4x²
=4x(1-x)

armaan

but here its given that x<1/rt2.... even if v put x/rt2 in this eqn .... 1-2x ....

=1-rt2..

the sq won't exist !!??

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