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

Question

The probability that a number n chosen at random from 1 to 30, to satisfy n+(50/n)>27 is (A)  7/30  (B)  3/10  (C)  3/5  (D)  1/5

Tardigrade Admin · Accepted Answer

Total outcomes =30 Now, n+(50+n)>27 ⇒ n2-27n+50>0 ⇒ (n-2) (n-25)=0 Favourable outcomes are 1,26,27,28,29,30. Number of favourable outcomes = 6 ∴ Required probability =(6/30)=(1/5)

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

$7/30$

$3/10$

$3/5$

$1/5$

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

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

7/30

3/10

3/5

1/5