Question

A coin is tossed. If it shows head, we draw a ball from a bag consisting of $3$ blue and $4$ white balls; if it shows tail, we throw a die. Describe the sample space of this experiment.

Answer 1

Given:
A coin is tossed. If it shows head, we draw a ball from a bag consisting of $3$ blue and $4$ white balls; if it shows tail, we throw a die.
If a coin is tossed then possible outcomes are $(H,T)$
If a dice is thrown then possible outcomes are $(1,2,3,4,5,6)$
If it shows head then we draw a ball from a bag consist of $3$ blue $(B_1,B_2,B_3)$ balls & $4$ white $(W_1,W_2,W_3,W_4)$ balls.
So, sample space if it is head is
$S_H=\{H{B}_1,H{B}_2,H{B}_{3}H{W}_1,H{W}_2,H{W}_3,H{W}_4\}\cdots \left(i\right)$
if it shows tail we throw a die.
So, sample space if it is tail is
$S_T=\{T1,T2,T3,T4,T5,T6\}\cdots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$
The sample space is $S=\{H{B}_1,H{B}_2,H{B}_3,H{W}_1,H{W}_2,H{W}_3,H{W}_4,T1,T2,T3,T4,T5,T6\}$.