Question

A die is rolled and then a coin is tossed. What is the sample space for this experiment?

• A. $S=\{1,2,3,4,5,6,H,T\}$
• B. $S=\{1H,2H,3H,4H,5H,6H\}$
• C. $S=\{1T,2T,3T,4T,5T,6T\}$
• D. $S=\{1H,2H,3H,4H,5H,6H,$
  $1T,2T,3T,4T,5T,6T\}$

Answer 1

The correct option is D $S=\{1H,2H,3H,4H,5H,6H,$

$1T,2T,3T,4T,5T,6T\}$
When a die is rolled, the possible outcomes are $1,2,3,4,5$ and $6$.

Sample space when a die is rolled is:
$S_1=\{1,2,3,4,5,6\}$

When a coin is tossed, the possible outcomes are head$\left(H\right)$ and tail$\left(T\right)$.

Sample space when a coin is tossed is:
$S_2=\{H,T\}$

Sample space $S$ for rolling a die and then tossing a coin would be obtained by combining $S_1$ and $S_2$.

$S=\{1H,2H,3H,4H,5H,6H,$
$1T,2T,3T,4T,5T,6T\}$

Therefore, option (d.) is the correct answer.