Question

What is the probability of choosing a square between 2 and 100 (both number inclusive)?
(a) \[\dfrac{1}{11}\]
(b) \[\dfrac{1}{10}\]
(c) \[\dfrac{8}{11}\]
(d) \[\dfrac{9}{100}\]

Answer 1

Hint: Find the number of squares from 2 to 100 both numbers inclusive. This can be done by considering numbers from 2 to 10 and taking their squares. Find the total number from 2 to 100. Probability is obtained as the total number of squares by total possible outcome.

Complete step by step solution:
We need to find the probability of choosing a square number between 2 and 100. A square number is a perfect square i.e. integer that is the square of an integer. It is the product of some integer with itself. Let us first look into the square number starting from 2.
\[\begin{align}
  & {{2}^{2}}=4 \\
 & {{3}^{2}}=9 \\
 & {{4}^{2}}=16 \\
 & {{5}^{2}}=25 \\
 & {{6}^{2}}=36 \\
 & {{7}^{2}}=49 \\
 & {{8}^{2}}=64 \\
 & {{9}^{2}}=81 \\
 & {{10}^{2}}=100 \\
\end{align}\]
Now we got 9 square numbers, we can include 2 and 100 in this as it is mentioned that both numbers are inclusive. After \[{{10}^{2}}\] the number is greater than 100. Thus they cannot be included in finding the probability. So here we have the total number of square numbers from 2 to 100, both inclusive as 9.
Now we know that the total number of numbers from 2 to 100 = 99.
Hence required probability = Total number of favorable outcomes / Total number of outcomes.
Probability of choosing a square number between 2 and 100 = Total number of square number between 2 and 100 / Total numbers from 2 to 100
= \[\dfrac{9}{99}=\dfrac{1}{11}\]
Thus we got the required probability as \[\dfrac{1}{11}\].
Thus option (a) is the correct answer.

Note: The question may confuse you as it is first to find probability between 2 and 100 and the mentioned both numbers inclusive. Thus don’t forget to take 2 and 100 while calculating total numbers between 2 and 100. You might get the answer wrong if you don’t take it correctly.