Question

One die of red colour $(R)$, one of white $\operatorname{colour}(W)$ and one of blue colour $(B)$ are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Then, the sample space is

• A. $S=\begin{Bmatrix}R 1 . & R 2, & R 3, & R 4, & R 5, & R 6 \\ W 1, & W 2 . & W 3, & W 4, & W 5, & W 6 \\ B 1 . & B 2, & B 3, & B 4, & B 5, & B 6\end{Bmatrix}$.
• B. $S=\begin{Bmatrix}R 1, & R 2 & R 3, & R 4, & R 5 & R 6 \\ W 1, & W 2, & W 4, & W 5 & & \\ B 1 . & B 3, & B 4, & B 5 & B 6 & \end{Bmatrix}$
• C. Both (a) and (b)
• D. None of the above

Answer 1

Answer: (A)

Let $R, W$ and $B$ denote the red, white and blue die respectively. When a die will be selected, then there will be possibilities for colour $R, B$ or $W$. But there will be 6 possibilities for 6 numbers ( 1 to 6 ) with each colour. So, the sample space is
$S=\begin{Bmatrix}R 1 . & R 2, & R 3, & R 4, & R 5, & R 6 \\ W 1, & W 2 . & W 3, & W 4, & W 5, & W 6 \\ B 1 . & B 2, & B 3, & B 4, & B 5, & B 6\end{Bmatrix}$.