Question

Write S and n(S) when a coin is tossed and a die is rolled simultaneously?

Answer 1

Hint: It is given that a coin is tossed and die is rolled simultaneously . the number of possible outcomes in tossing a coin is 2 and the number of possible outcomes of rolling a die is 6. Therefore the number of possible outcomes when both occur simultaneously is 2*6.

Complete step-by-step answer:
We are given that a coin is tossed and a die is rolled simultaneously
So when a coin is tossed the number of possible outcomes is 2
That is , head and tail
And when a die is rolled the number of possible outcomes is 6
That is , { 1 , 2 , 3 , 4 , 5 , 6 }
When both are done simultaneously then the number of possible outcomes = 2*6 = 12
Therefore,
$S = \left\{ \begin{gathered}
  \left( {head,1} \right),\left( {head,2} \right),\left( {head,3} \right),\left( {head,4} \right),\left( {head,5} \right),\left( {head,6} \right) \\
  \left( {tail,1} \right),\left( {tail,2} \right),\left( {tail,3} \right),\left( {tail,4} \right),\left( {tail,5} \right),\left( {tail,6} \right) \\
\end{gathered} \right\}$
And n(S) = 12

Note: The sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.
In probability the number of elements in the sample space of tossing n coins simultaneously is ${2^n}$.
And the number of elements in the sample space of rolling n dice simultaneously is ${6^n}$.