Find the probability that the sum of n numbers is divisible by n ,,assuming n is very large no.

a)1 b) 1/2 c) 3/4 d) None of these e)Can't be determined.

• sum of n numbers is n(n+1)/2
  case 1)when n is odd take 3
  Sum is 3*4/3 it is divisible by 3
  we can conclude that n=odd sum of n numbers is divisible by n
  case2) when n is even take 4
  Sum is 4*5/2=>10 10/4 rem is 2 so not divisible
  we can conclude that n=even sum of n numbers is not divisible by n
  Total of total 2 cases 1 case is possible
  So probability=possible/total=1/2
  Ans--1/2
• 8 years agoHelpfull: Yes(43) No(2)
• n*(n+1)/2 is always divisible by n for this (n+1)/2 must be integer so n should be odd that's why answer is 1/2.
• 8 years agoHelpfull: Yes(6) No(2)
• n*(n+1)/2 is always divisible by n
  so probability is one
  answer a
• 8 years agoHelpfull: Yes(5) No(17)
• This is a bit confusing for me.
  It is not mentioned "Sum of first n natural numbers" or "consecutive numbers".
  If the n numbers are randomly selected then the solution can't be determined.
  If n is consecutive probability is 0.5.
• 7 years agoHelpfull: Yes(1) No(0)
• n(n+1)/2 , which is always divisible by n
  so, the prob. will be always 1
• 7 years agoHelpfull: Yes(0) No(3)