Question

The probability of getting a composite number on the throw of a dice is:
\[
  A.\dfrac{1}{3} \\
  B.\dfrac{5}{6} \\
  C.\dfrac{1}{2} \\
\]
D. None of these

Answer 1

Hint: We will consider a sample space and the favourable outcomes individually to avoid any kind of mistake. A composite number is a non prime number.

Complete step-by-step answer:
We are asked to find the probability of getting a composite or non prime number when we throw a dice.
When we throw a dice, the number of outcomes which are possible are \[6\].
The sample space \[S\] of the event is\[\left\{ {1,2,3,4,5,6} \right\}\].
There are 2 composite or non prime numbers in the sample space which are \[\{ 4,6\} \].
So, the number of favourable outcomes which are possible \[ = 2\]
Let \[A\] be the event of getting composite numbers when we throw a dice.
So, the probability of getting composite numbers when we throw a dice
\[
   = P(A) \\
   = \dfrac{{n(A)}}{{n(S)}} \\
   = \dfrac{2}{6} \\
   = \dfrac{1}{3} \\
\]
\[n(A)\& n(S)\]are the cardinal numbers of the event of getting composite numbers when we throw a dice and the sample space respectively.
Therefore, the probability of getting a composite number on throwing a dice is \[\dfrac{1}{3}\].
Thus, the answer is option A.

Note: We use the formula P(an event)\[ = \dfrac{{n(A)}}{{n(S)}}\]where A is the event, n(A) is the number of favourable outcomes and n(S) is the total number of possible outcomes. In these types of questions, we will always use the simple probability method in order to avoid making any mistakes.