Question

The sample space for the experiment where a coin is tossed and then a die is rolled only in case a head is shown on the coin is:

• A. $\{H1,H2,H3,H4,T\}$
• B. $\{H,T1,T2,T3,T4,T5,T6\}$
• C. $\{H1,H2,H3,H4,H5,H6,T\}$
• D. $\{H1,H2,H3,H4,H5,H6\}$

Answer 1

The correct option is C $\{H1,H2,H3,H4,H5,H6,T\}$

Since either coin can turn up Head $\left(H\right)$ or Tail $\left(T\right)$, these are the possible outcomes for the coin tossed.
Let us assume that $1,2,3,4,5$ and $6$ are possible number that come when the die is thrown.
When head is encountered, then, number of elements in sample space $=(1\times 6)=6$
$\therefore$ Sample space in case head is encoutered is, $S_H=\{H1,H2,H3,H4,H5,H6\}$
Now, when tail is encountered sample space $S_T=\left\{T\right\}$
Therefore the total sample space $S=\{H1,H2,H3,H4,H5,H6,T\}$