JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Probability

Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space

[0, 60]

is less than or equal to a. If

P (A) = \frac{11}{36}

, then a is equal to ______.

Answer: 10

Solution

Choosing two numbers in

[0, 60]

corresponds to a point in the square of area

3600.

The event

∣ x - y ∣ \leq a

is the band between

y = x - a

and

y = x + a

, whose area is the square less two corner triangles of legs

60 - a

: namely

3600 - (60 - a)^{2} .

Then

P (A) = \frac{3600 - ( 60 - a ) ^{2}}{3600} = \frac{11}{36}

gives

(60 - a)^{2} = 2500

, so

60 - a = 50

and

a = 10.

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer