Question

A bag contains one white and one red ball. A ball is drawn from the bag. If the ball drawn is white, it is replaced in the bag and again a ball is drawn. Otherwise a die is tossed. Write the sample space for this experiment.

Answer 1

Hint: Sample space is the set of all possible outcomes of an experiment. Consider all the cases and write the corresponding outcomes.

Complete step-by-step answer:
An experiment is defined as an action or operation resulting in two or more outcomes. For the given experiment, we have to calculate all the possible outcomes.
So, step by step we will perform the experiment as given in the question and we will make a tree diagram to have a clear visualization.
At first, we have to draw a ball from the given bag which contain one white and one red ball, two possible outcomes:

1.Let us denote the outcome that the drawn ball is white by ‘W’.
2.Let us denote the outcome that the drawn ball is Red by ‘R’.
Now, according to the question, if the replaced ball is white, it is replaced in the bag and again a ball is drawn.

But if at first the red ball is drawn, a die is tossed.

Now, we can write the total outcomes by completing the whole tree diagram.

All possible outcomes –
1){W,W}
2){W,R}
3){R,1}
4){R,2}
5){R,3}
6)[R,4}
7){R,5}
8){R,6}
There are total ‘8’ possible outcomes.
Where, W = an outcome of drawing white ball.
R = an outcome of drawing Red ball.
I = an outcome of getting ‘I’ after tossing a die.
Where $1\le i\le 6$ .
Note: Complete the tree diagram carefully to get all the possible outcomes. Another approach is to write down all the possible outcomes cases and combine to get the sample space.