Question

If a number is selected at random from the numbers from 1 to 100, then what is the probability that it is a multiple of 10?
A) $\dfrac{1}{5}$
B) $\dfrac{1}{{20}}$
C) $\dfrac{1}{{10}}$
D) $\dfrac{1}{{40}}$

Answer 1

Hint:
Here we find the total number of observations and find the number of multiples of 10 that lie in between 1 to 100 and then using the formula of probability we find probability of a number being multiple of 10.
Probability of an event is defined as the number of possible outcomes divided by total number of observations.

Complete step by step solution:
We are given the numbers 1 to 100.
So, the total number of observations is100.
Now we have to find numbers lying in 1 to 100 that are multiples of 10.
10 is a multiple of a number if that number can be written as $10 \times n$, where n is another multiple of the number.
So, we write multiples of 10
$10 \times 1 = 10$
$10 \times 2 = 20$
$10 \times 3 = 30$
$10 \times 4 = 40$
\[10 \times 5 = 50\]
\[10 \times 6 = 60\]
\[10 \times 7 = 70\]
\[10 \times 8 = 80\]
\[10 \times 9 = 90\]
\[10 \times 10 = 100\]
\[10 \times 11 = 110\]
and so on.
But we have to find multiple of 10 between the numbers 1 to 100.
From the list of multiples of 10 we see that multiples of 10 lying in the list 1 to 100 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 only.
So, the number of possible outcomes is 10.
Now we can use the formula for probability of an event which implies the number of possible outcomes divided by the total number of observations.
 Probability $ = \dfrac{{10}}{{100}}$
Probability $ = \dfrac{{10}}{{10 \times 10}}$
Now we cancel out the similar terms from the numerator and denominator.
Probability $ = \dfrac{1}{{10}}$
So, the correct answer is “Option C”.

Note:
The most common mistakes done by students is in writing probability in a form where the fraction is not in simplest form which is wrong because probability should always be written in simplest form of fraction. Also, as probability of an event is always greater than or equal to zero and less than or equal to one, we need to check this properly after calculating the probability. If the above conditions are not met then our answer is incorrect.