Question

A die is thrown. If A is an event of getting an odd number, then write the sample space and event A in set notation.

Answer 1

Hint: Given that a die is thrown once, the die is the shape of the cube so it has 6 faces and numbered as 1, 2, 3, 4, 5, 6. By this, we can get the sample space of the given event. Given A is an event of getting odd numbers so write the desired in set notation.

Complete step-by-step solution -
If a die is thrown once then the total number of possible outcomes is 6
They are 1, 2, 3, 4, 5, 6
Let S be the sample space when the die is thrown once
\[S=\left\{ 1,2,3,4,5,6 \right\}\]. . . . . . . . . . . . . . . . (1)
Let A is the event of getting an odd number
Among all the possible outcomes when die is thrown once the odd numbers are 1, 3, 5.
\[A=\left\{ 1,3,5 \right\}\]. . . . . . . . . . . . . . . . . . . . (2)

Note: In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of the given experiment. An event is said to occur on a particular trial of the experiment. An event is always a subset of the sample space. When a die is thrown once the number of possible outcomes is six and when die is thrown twice the total number of possible outcomes is 36. So the total number of possible outcomes when die is thrown n times is \[{{6}^{n}}\].