Question

What is the probability of choosing a square between 2 and 100 (both numbers inclusive)?
A.$\dfrac{1}{{11}}$
B. $\dfrac{1}{{10}}$
C. $\dfrac{8}{{11}}$
D. $\dfrac{9}{{100}}$

Answer 1

We count the total number of squares between 2 and 100 and use the formula of probability to calculate the probability of choosing the number from total numbers.

• Square of a number is the value that is obtained when the number is multiplied to itself.
• Probability of an event is given by the number of possibilities divided by total number of possibilities.

Complete step-by-step answer:
Since, we have the numbers from 2 to 100, the total number of outcomes is 99.
Now, we write the possible outcomes.
Since, possible outcomes are the values that are square between 2 and 100, we can write the possibilities as
${2^2} = 4;{3^2} = 9;{4^2} = 16;{5^2} = 25;{6^2} = 36;{7^2} = 49;{8^2} = 64;{9^2} = 81;{10^2} = 100$
So, the number of possible outcomes is 9.
Now, we know that the probability of an event is given by the number of possibilities divided by the total number of possibilities.
Here, the total number of outcomes is 99 and the possible number of outcomes is 9.
$\Rightarrow$Probability $= \dfrac{9}{{99}}$
Cancel the same factors i.e. 9 from numerator and denominator of the fraction.
$\Rightarrow$Probability $= \dfrac{1}{{11}}$
$\therefore$ The probability of choosing a square between 2 and 100 is $\dfrac{1}{{11}}$.

$\therefore$Option A is correct.

Note:
Many students make mistake of writing the total number of outcomes as 98 as they use the method $100 - 2 = 98$ which is wrong as in this method we count one of the numbers on the edge but here we are given the word inclusive which means that both the numbers are included so we count the total number of outcomes as 99. Also, keep in mind the probability value should be in lowest form.