Question

A coin tossed and then a die is thrown. Describe the sample space for this experiment.

Answer 1

Hint: In order to find the sample, find the sample space of the above event, identify all the random experiments and their outcomes. Coin has two outcomes , one is HEAD and other is TAIL, and after any outcome of coin , a die is compulsorily thrown which has outcomes 1,2,3,4,5,6.

Complete step-by-step answer:
Here our question says a coin is tossed and then a die is thrown and we have drawn the sample space of the experiment.
On the first, we have to identity the random experiments
So the first random experiment is tossing a coin Which we give result either Head or Tail.
After this a dice is thrown,
Now, if we consider that the result of coin was HEAD, a die is thrown whose result can be
1,2,3,4,5,6
And similarly, if result of coin was TAIL then also the die was thrown
1,2,3,4,5,6,
So now let’s form the sample space of this random experiment we get
Sample Space
$ S = $ \[\left\{
  \left( {H,1} \right),\left( {H,2} \right),\left( {H,3} \right),\left( {H,4} \right),\left( {H,5} \right),\left( {H,6} \right) \\
  \left( {T,1} \right),\left( {T,2} \right),\left( {T,3} \right),\left( {T,4} \right),\left( {T,5} \right),\left( {T,6} \right) \;
  \right\}\]
Here H represents HEADS and T represents T.

Note: 1. A random Experiment is basically a mechanism which produces some definite result or outcomes that cannot be predicted with any certainty.
2. The Sample space is associated with a random experiment which generates the set of all the possible outcomes in an event .
3. Probability of getting a head or tail for tossing a coin is $ \dfrac{1}{2} $ and the probability of getting any number during a die throw is $ \dfrac{1}{6} $ .