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  4. The probability that a number n chosen at random from 1 to 30, to satisfy n+(50/n)>27 is

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Q. The probability that a number n chosen at random from 1 to 30, to satisfy $ n+(50/n)>27 $ is

J & K CETJ & K CET 2006

Solution:

Total outcomes $ =30 $ Now, $ n+(50+n)>27 $
$ \Rightarrow $ $ {{n}^{2}}-27n+50>0 $
$ \Rightarrow $ $ (n-2)\,(n-25)=0 $
Favourable outcomes are 1,26,27,28,29,30. Number of favourable outcomes = 6
$ \therefore $ Required probability $ =\frac{6}{30}=\frac{1}{5} $