Question

There are three coloured dice of red, white and black colour. These dice are placed in a bag. One die is drawn at random from the bag and rolled, its colour and the number on its uppermost face is noted. Describe the sample space for this experiment.

Answer 1

Since we have 3 coloured dice
1 - red dice
1 - white dice and
1 - black dice

Now, one of the dice is drawn and tolled and the number of the face is noted. So, in case red dice is drawn then the sample will be

$S_1$ = {(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6)}

Similar argument for black dice

$S_2$ = (B, 1 ), (B, 2), (B, 3), (B, 4), (B, 5) (B, 6)}

and for while dice

$S_3$ = {(W, 1), (W, 2), (W, 3), (W, 4), (W, 5), (W, 6)}

Thus, the Sample space associated uitli this experiment is

$S=S_1\cup S_2\cup S_3$

={(R, 1) (R, 2),(R, 3),(R, 4), (R, 5), (R,6)
(B, 1), (B, 2), (B. 3), (B, 4), (B, 5), (B, 6),
(W, 1), (W, 2), (W, 3), (W, 4), (W, 5), (W, 6)}