Question

Define a random experiment.

Answer 1

Hint:A Random Experiment is an experiment, trial, or observation that can be repeated numerous times under the same conditions. The outcome of an individual random experiment must be independent and identically distributed.

Complete step by step answer:
Examples of a Random experiment include:
The tossing of a coin. The experiment can yield two possible outcomes, heads or tails.
The role of a die. The experiment can yield six possible outcomes, this outcome is the number 1 to 6 as the die faces are labeled
Before rolling a die you do not know the result. This is an example of a random experiment. In particular, a random experiment is a process by which we observe something uncertain. After the experiment, the result of the random experiment is known. An outcome is a result of a random experiment.

 The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set.

Here are some examples of random experiments and their sample spaces:
Random experiment: toss a coin; sample space$$$$or as we usually write it, $$$$Random experiment: roll a die; sample space: $$S=\left\{\text{1},\text{2},\text{3},\text{4},\text{5},\text{6}\right\}.$$Random experiment: observe the number of iPhones sold by an Apple store in Boston in$$\text{2}0\text{15}$$; sample space: $$S=\{0,\text{1},\text{2},\text{3},\cdots \}.$$
Random experiment: observe the number of goals in a soccer match; sample space: $$S=\{0,\text{1},\text{2},\text{3},\cdots \}.$$

Note:
The sample space is defined based on how you define your random experiment.
Outcomes of the random experiment are independent of each other. For example: if we toss a coin 2 times the possibility of the appearance of head and tails is equal in both turns.
Let us suppose that when the head appears in the first throw it does not affect the probability of the next throw in any way.