Before rolling a die, the outcome is unknown. 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 outcome 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 the universal set. And, an event is a subset of the sample space to which a probability is assigned. When a random experiment is repeated several times, each one of them is called a trial. Thus, a trial is a particular performance of a random experiment.
Random Experiment: A process by which we observe something uncertain.
Outcome: A result of a random experiment.
Sample Space: The set of all possible outcomes.
Event: A subset of the sample space.
Trial: If we repeat a random experiment 3 times, then these are three trials.
A coin is tossed two times. What is the probability that both times the head was occurred?
The process of rolling a coin two times is a random experiment.
The trial 1 is rolling the coin first time, and the trial two is rolling the dice second time. Together these two trials form a random experiment.
Suppose in the first trial, the “head” was occurred. So, the “head” is the outcome of the first trial. And, suppose that a “tail” was occurred on the second trial. So, the outcome of the second trial is a “tail”.
It is possible that “head” is occurred on both of the trials or “tail” occurred both times. It is also possible that “head” occurred first time and “tail” occurred the second time. Similarly, “tail” can occur the first time and the “head” can occur the second time. So, the sample space (a set of all possible outcomes) can be given as
Now, what is the probability that both times the head was occurred? So, the event is “Head on both of the trials”. This is the event, we want to assign a probability.