A number n is chosen at random from s= 1,2,3, , 50 . Let A = n s: n is a square , B = n s: n is a prime and C = n s: n is a square . Then, correct order of their probabilities is

Step-by-step solution

Given, S= 1,2,3 , 50 aligned A & + n S: n+ 50 n >27 & = n S: n^2-27 n+50>0 & = n S:(n-25)(n-2)>0 & = n S: n 25 & = 1,26,27,28, , 50 aligned aligned & n(A)=26 & B= n S: n is prime & = 2,3,5,7,11,13,17,19,23 , & 29,31,37,41,43,47 & n(B)=15 & C= n S: n is a square = 1,4,9,16,25,36,49 & n(C)=7 & p(A)= n(A) n(S) = 26 50 , & p(B)= n(B) n(S) = 15 50 , & p(C)= n(C) n(S) = 7 50 & p(A)>p(B)>p(C) & aligned