A number$\ n\$is chosen at random from $S = \left\{ 1,\ 2,\ 3,\ \ldots,\ 50 \right\}.$ $Let\ A = \left\{ n \in S:n + \frac{50}{n} 27 \right\},\ B = \left\{ n \in S:n\ is\ a\ prime \right\}\ and\$ $C = \left\{ n \in S:n\ is\ a\ square \right\}.\$Then, correct order of their probabilities is

Question

A number$\ n\$is chosen at random from $S = \left\{ 1,\ 2,\ 3,\ \ldots,\ 50 \right\}.$ $Let\ A = \left\{ n \in S:n + \frac{50}{n} > 27 \right\},\ B = \left\{ n \in S:n\ is\ a\ prime \right\}\ and\$ $C = \left\{ n \in S:n\ is\ a\ square \right\}.\$Then, correct order of their probabilities is

Dr. Abubacker · Accepted Answer

(b)
Given, $S = \{ 1,2,3\ldots,50\}$
$A = \left\{ n \in S:n + \frac{50}{n} > 27 ight\}$
$= \{ n \in S:n^{2} - 27n + 50 > 0\}$
$= \{ n \in S:n < 2\ or\ n > 25\}$
$= \{ 1,\ 26,\ 27,\ldots,\ 50\}$
$\Rightarrow \ n(A) = 26$
$B = \{ n \in S:n\ is\ a\ prime\}$
$= \{ 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47\}$
$\Rightarrow \ n(B) = 15$
$	herefore\ C = \{ n \in S:n\ is\ a\ square\}$
$= \{ 1,4,9,16,25,36,49\}$
$\Rightarrow \ n(C) = 7$
$	herefore\ P(A) = \frac{n(A)}{n(S)} = \frac{26}{50},P(B) = \frac{15}{50},P(C) = \frac{7}{50}$
$\Rightarrow \ P(A) > P(B) > P(C)$

Q. A number$\ n\$is chosen at random from $S = \left\{ 1,\ 2,\ 3,\ \ldots,\ 50 \right\}.$ $Let\ A = \left\{ n \in S:n + \frac{50}{n} > 27 \right\},\ B = \left\{ n \in S:n\ is\ a\ prime \right\}\ and\$ $C = \left\{ n \in S:n\ is\ a\ square \right\}.\$Then, correct order of their probabilities is

Explanation

Reviewed by Dr. Abubacker

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