A natural number is chosen at random from the first 100 natural numbers. The probability that x+100x>50 is

We have,x+100x>50or  x2+100>50xor  (x−25)2>525⇒x−25<525 or x−25>525⇒x<25−525 or 25+525 As x is a positive integer and 525=22.91, we must have x≤2 or x≥48. Thus, the favorable number of cases is 2+53==55 Hence, the required probability is 55/100=11/20.