Question

# A die is thrown. Write the sample space. If A is the event that the number is a perfect square, write the event A using set notation.

Hint: to solve this question we will find all the possible outcomes we can get on throwing the die. And for event A we will see from all outcomes, which numbers are perfect squares and then we will denote the Sample space and event A in set notation.

Complete step by step answer:
Before solving the question let us first understand the terms die, sample space, event and set notation form.
A die is a cubical shaped object on which a number of dots are marked where the number is from 1 to 6. Die is used in throwable games and board games.
In probability, the sample space of an experiment or any random trial is a set or collection of all possible outcomes or results of that experiment.
In probability, an event is a set of outcomes of an experiment to which probability is assigned.
Set notation is generally notation of objects in curly brackets that is in { }.
Now, we have given that dice are thrown. So, all possible outcomes will total numbers mentioned on it which are 1, 2, 3, 4, 5, 6.
So, sample space = { 1, 2, 3, 4, 5, 6 }
Now, there is an event A which is defined as the number is a perfect square. In sample space { 1, 2, 3, 4, 5, 6 }, there are only two perfect squares which are 1 and 4 as ${{\text{1}}^{\text{2}}}\text{=1, }{{\text{2}}^{\text{2}}}\text{=4}$.
So, Event A = { 1, 4 }

Note: as the question is basic of probability so one must know the meaning of sample space, event, probability, collection etc. When we represent the collection of objects in a set, always write the objects in curly brackets, that is objects must be placed in { }.