Let A be the event that the absolute difference between two randomly chosen real numbers in the sample space 0 , 60 is less than or equal to a . If P A = 11 36 , then a is equal to _____ .

Step-by-step solution

Given, A be the event that the absolute difference between two randomly chosen real numbers in the sample space 0 , 60 is less than or equal to a , So, x - y < a ⇒ - a < x - y < a ⇒    x - y < a and x - y > - a Now on plotting the diagram we get, Now from diagram probability is given by, P A = area ( OACDEG ) area ( OBDF ) ⇒ P A = area OBDF - area ABC - area EFG area OBDF ⇒    11 36 = 60 2 - 1 2 60 - a 2 - 1 2 60 - a 2 3600 ⇒    1100 =