Cards marked with numbers 3,4,5, ..........., 50 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on the drawn card is a number which is a perfect square.

A
$\frac{3}{7}$
B
$\frac{2}{7}$
C
$\frac{1}{8}$
D
$\frac{1}{7}$

Solution:

It is given that the box contains cards marked with the number 3,4,5,.......,50.
So, the total number of outcomes is 50 - 2 = 48.
The probability P(E) of the random experiment as,

$P (A) = \frac{Number of favorable outcomes}{Total number of outcomes}$
The number of events getting cards of perfect square is,
n(X) = {4,9,16,25,36,49}

$\Rightarrow$ Number of favorable outcomes = 6
So, the probability of getting cards of a perfect square is,