Probability Question 214
Question: A natural number is chosen at random from the first 100 natural numbers. The probability that $ x+\frac{100}{x}>50 $ is
Options:
A) 1/10
B) 11/50
C) 11/20
D) none of these
Show Answer
Answer:
Correct Answer: D
Solution:
We have, $ x+\frac{100}{x}>50 $ Or $ x^{2}+100>50x $ Or $ {{(x-25)}^{2}}>525 $
$ \Rightarrow x-25<\sqrt{525} $ or $ x-25>\sqrt{525} $
$ \Rightarrow x<25-\sqrt{525} $ or $ 25+\sqrt{525} $
As x is a positive integer and $ \sqrt{525}=22.91 $ , we must have $ x\le 2 $ or $ x\ge 48. $
Thus, the favorable number of cases is 2+53=55. Hence, the required probability is 55/100=11/20.
BETA
