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# A bag contains tickets numbered 1 to 20. Two tickets are drawn from the bag. The probability that both the numbers appearing on the tickets drawn will be prime is :

$\begin {array} {1 1} (1)\;\large\frac{17}{95} & \quad (2)\;\large\frac{12}{95} \\ (3)\;\large\frac{14}{95} & \quad (4)\;None\: of\: these \end {array}$

The prime numbers lying in [1,20] are
2, 3, 5, 7, 11, 13, 17, 19
$\therefore$ Totally we have 8 numbers
Hence the required probability is
$\large\frac{8C_2}{20C_2} = \large\frac{28}{190}$
$= \large\frac{14}{95}$
Ans : (3)