Question

There are tickets numbered from $1$ to $30$ in a box. A ticket is drawn at random from the box and if $A$ is the event that the number on the ticket is a multiple of five. Write the sample space $s$, $n(s)$, the event $A$ and $n(A).$

Answer 1

Here we are going to use the reference Sample space for the given event A to occur and its number of possibilities.

Complete step by step solution:
There are $30$ tickets in the box.
As we know that, Sample space is the range of an experiment or the random trial is the set of all possible outcomes or results of that experiment.
Let $S$ be the sample space.
Therefore, $S = \\{ 1,2,3,...30\\}$
$\therefore n(S) = 30$
Now, Let A be the event that the number on the ticket is a multiple of five
$\begin{array}{l} \therefore A = \\{ 5,10,15,20,25,30\\} \\\ \therefore n(A) = 6 \end{array}$

Additional information: The probability is the ratio of the favourable outcomes to the total number of all the possible outcomes.
$P(A) = \frac{{n(A)}}{{n(S)}}$

Note: Read the event entitle for the given event and possible outcomes accordingly for example; multiple of five, even numbers, odd numbers, prime numbers and so on... note down the relevant numbers from the reference sample space.