Question

There are 30 tickets in a box numbered from 1 to 30. A ticket is drawn out at random. Let A be the event that the number on the ticket is a multiple of 6. Write the sample set of S & outcomes of event A in set form.

Answer 1

There are 30 tickets in a box (numbered from 1 to 30). To find the outcomes of A which is the event that the number on the ticket is a multiple of 6. So, we just write the numbers divisible by 6 from 1 to 30 in set form. Total no of observations in the sample set will be the required outcomes of event A.So we will get the answer to this problem.

Complete step by step solution: It is given that there are 30 tickets in the box and a ticket is drawn at random.
Let S be the sample set.
\left( S \right)=\left\\{ 1,\ 2,\ 3,\ 4,\ \ldots \ldots \ldots \ldots \ldots \ldots \ldots ,\ 30 \right\\}
This is a sample set because any ticket from 1 to 30 can be drawn randomly.
$\therefore n(S)=3\to$ (n(S) no of elements in a S).
and the sample space is also known as a sample set.
Given: Let A be the event that the number on the ticket is a multiple of 6.
Therefore outcomes of the event A will be the numbers from 1 to 30 which are divisible by 6.
Set A contains following numbers:
\left( A \right)=\left\\{ 6,\ 12,\ 18,\ 24,30 \right\\}.
Outcomes of Sample set A is {6, 12, 18, 24, 30} or event A.

Note: Here are the definitions of the following terms that you should Know:

1. Sample space: The sample space of an experiment is all the possible outcomes for that experiment.
2. Event: An event is a set of outcomes of an experiment.