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The probability of getting a perfect square number from the numbers $1$ to $10$ is
$A)$$\dfrac{3}{{10}}$
$B)$$\dfrac{1}{2}$
$C)$$\dfrac{2}{5}$
$D)$$\dfrac{1}{5}$

seo-qna
Last updated date: 13th Jul 2024
Total views: 348.3k
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Answer
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Hint: First we have to define what the terms we need to solve the problem are.
First of all, we just need to know such things about the 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 $\sqrt 1 = 1$ or $1 = {1^2}$

Complete step by step answer:
Since the given question is to obtain the perfect square numbers from the numbers $1$ to $10$
It means we need to check which numbers are perfect square numbers from one to ten.
First write the or take the square root of the natural numbers from the numbers $1$ to $10$and then we have to count the numbers that are perfect square, since the perfect square is the square of whole numbers, we will first define the square root of natural numbers (difference between whole and natural number is zero is contained in whole number and not in the natural number) thus in the given question there is no zero.
Hence let us see the perfect numbers from, $\sqrt 1 = 1$ or $1 = {1^2}$ (since one square is one and square root of the one is one) and now $\sqrt 4 = 2$(or also the two square is four which Is a perfect square)
And the final perfect square is $\sqrt 9 = 3$(also the square root of three is nine)
Therefore, we have three perfect squares from the numbers $1$ to $10$ which are $\sqrt 1 = 1$,$\sqrt 4 = 2$ and $\sqrt 9 = 3$
Hence, we need to find the probability of getting a perfect square number from the numbers $1$ to $10$ is
Probability = favorable events divided by total events and hence probability = $\dfrac{3}{{10}}$ (three is the favorable and total is ten) therefore the probability of getting a perfect square number from the numbers $1$ to $10$ is $\dfrac{3}{{10}}$
So, the correct answer is “Option A”.

Note: Since the total number of getting the probability is ten all other options like $B)$$\dfrac{1}{2}$,$C)$$\dfrac{2}{5}$,$D)$$\dfrac{1}{5}$ will be eliminated as the perfect square is three. If the given question has the word from one to ten then we must exclude the perfect square of one (ten is not a perfect square). So, then we get two perfect squares only.