 Question

# Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2 Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2

CAT 2021

A
B
C
D
##### 1/2
Solution

Correct option is

(A)

we have given ,Region R is the triangle in the first quadrant with vertices (0,0) and (4,0) and (0,3) . The region R is the sample space. The area of the triangle is considered as it is a continuous distribution of points in the region .

Area of region R is 6 units.

Further the event is r>2 with r,s being a point in the region R. So our event is basically the triangle with vertices (2,0) and (4,0) and (2,1.5)

It's the common area bounded by r>2 and the region R. The area of the event triangle is 1.5 units.

Hence the probability is ratio of area of the event and area of the region R which is the sample space.

Hence probability is 1/4

so ,A is the correct option