Question

The probability that a number is selected at random from the numbers \[1,2,3....,15\] is a multiple of 4 is
A.\[\dfrac{4}{{15}}\]
B. \[\dfrac{2}{{15}}\]
C. \[\dfrac{1}{5}\]
D. \[\dfrac{1}{3}\]

Answer 1

Hint: Here we find the total number of observations and find the number of multiples of 4 that lie in between \[1,2,3....,15\] and then using the formula of probability we find probability of a number being multiple of 4.
* Probability of an event is given by the number of possible outcomes divided by total number of observations.

Complete step-by-step answer:
We are given the numbers \[1,2,3....,15\]
So, the total number of observations is \[15\].
Now we have to find numbers lying in \[1,2,3....,15\] that are multiples of \[4\].
\[4\] is a multiple of a number if that number can be written as \[4 \times n\], where n is another multiple of the number.
So, we write multiples of \[4\]
\[
  4 \times 1 = 4 \\
  4 \times 2 = 8 \\
  4 \times 3 = 12 \\
  4 \times 4 = 16 \\
 \]
and so on.
But we have to find multiple of \[4\] between the numbers \[1,2,3....,15\]
From the list of multiples of \[4\] we see that multiples of \[4\] lying in the list \[1,2,3....,15\] are \[4,8,12\] only.
So, the number of possible outcomes is \[3\].
Now we use the formula for probability of an event i.e. number of possible outcomes divided by total number of observations.
Probability \[ = \dfrac{3}{{15}}\]
Probability \[ = \dfrac{3}{{3 \times 5}}\]
Now we cancel out the same factors from the numerator and denominator.
Probability \[ = \dfrac{1}{5}\]

So, the correct answer is “Option C”.

Note: Students make mistakes 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, students should always check their answer off probability, because probability of an event is always greater than or equal to zero and less than or equal to one.