Question

A card is drawn from a pack of $100$ cards numbered $1$ to $100$. Then probability of drawing a number which is a square is
$A)\dfrac{1}{5}$
$B)\dfrac{2}{5}$
$C)\dfrac{1}{{10}}$
$D)$ None of these

Answer 1

First, we need to know the concept of probability and square numbers
Probability is the term mathematically with events that occur, which is the number of favorable events that divides the total number of outcomes.
The square numbers are the numbers that can be represented as the natural numbers after taking the square root.
Where the perfect square definition says perfect numbers, which is the numbers that obtain by multiplying any whole numbers (zero to infinity) twice, or the square of the given numbers yields a whole number like $\sqrt 4 = 2$ or $4 = {2^2}$
Formula used:
$P = \dfrac{F}{T}$where P is the overall probability, F is the possible favorable events and T is the total outcomes from the given.

Complete step-by-step solution:
Since from the given that we have, the card is drawn from a pack of $100$ cards numbered $1$ to $100$.
We need to find the probability of the square number of getting the cards.
Thus, the square numbers from numbered $1$ to $100$ are $1,4,9,16,25,36,49,64,81,100$ where these numbers can be represented into the form of ${1^2},{2^2},{3^2},{4^2},{5^2},{6^2},{7^2},{8^2},{9^2},{10^2}$.
We may also take the ${11^2} = 121$ but it will exceed the given condition pack of $100$ cards numbered $1$ to $100$
Hence the favorable events are $1,4,9,16,25,36,49,64,81,100 = 10$ events.
Also, the overall total events are given as $1,2,3,...,100 = 100$ events.
Hence by the probability formula, we have, $P = \dfrac{F}{T} = \dfrac{{10}}{{100}}$ where the favorable events are ten and the total outcome is a hundred.
Hence solving this we get $P = \dfrac{{10}}{{100}} \Rightarrow \dfrac{1}{{10}}$
Therefore, $C)\dfrac{1}{{10}}$ is correct.

Note: If we divide the probability value and multiplied with the number hundred, then we will get the percentage value for the required result. Which is $P = \dfrac{1}{{10}} = 0.1$ and now multiplying with the number hundred we get $P = 0.1 \times 100 \Rightarrow 10\%$. Hence the percentage of the square numbers from the card of numbered $1$ to $100$ is $10\%$