Question

O 60s Round 1 : 79 Q20 of 20 What is the probability that a point (x, y) chosen at random in the rectangle 1-1, 1] x [0, 1] is such that y > x??​

Answer 1

Answer:

Picking two points x and y randomly from the intervals [0,2] and [0,1] is equivalent to picking a single point (x,y) randomly from the rectangle S shown in the figure, which has vertices at (0,0) ,(2,0) , (2,1) and (0,1).So,we take S as our sample space.Now,the condition y≤x

2

is satisfied if and only if the point (x,y) lies in the shaded region.It is the portion of the rectangle lying below the parabola y=x

2

.Therefore, the required probability is given by

AreaoftherectangleS

Areaoftheshadedregion

Area of rectangle S=2 x 1=2.Area of shaded region is ∫

o

l

x

2

dx+1×1=

3

1

+

3

4

Hence,required probability is

2

3

4

=

3

2