What is a Statistical Experiment?
All statistical experiments have three things in common:

The outcome of the experiment depends on chance.
A coin toss has all the attributes of a statistical experiment. There is more
than one possible outcome. We can specify each possible outcome (i.e., heads or
tails) in advance. And there is an element of chance, since the outcome is
uncertain.
The Sample Space

An event is a subset of a sample space  one or more sample
points.
Types of events

Two events are independent when the occurrence of one does not
affect the probability of the occurrence of the other.
Sample Problems

Suppose I roll a die. Is that a statistical experiment?
Yes. Like a coin toss, rolling dice is a statistical experiment. There is more
than one possible outcome. We can specify each possible outcome in advance. And
there is an element of chance.

When you roll a single die, what is the sample space.
The sample space is all of the possible outcomes  an integer between 1 and 6.

Which of the following are sample points when you roll a die  3, 6, and 9?
The numbers 3 and 6 are sample points, because they are in the sample space.
The number 9 is not a sample point, since it is outside the sample space; with
one die, the largest number that you can roll is 6.

Which of the following sets represent an event when you roll a die?
A. {1}
B. {2, 4,}
C. {2, 4, 6}
D. All of the above
The correct answer is D. Remember that an event is a subset of a sample space.
The sample space is any integer from 1 to 6. Each of the sets shown above is a
subset of the sample space, so each represents an event.

Consider the events listed below. Which are mutually exclusive?
A. {1}
B. {2, 4,}
C. {2, 4, 6}
Two events are mutually exclusive, if they have no sample points in common.
Events A and B are mutually exclusive, and Events A and C are mutually
exclusive; since they have no points in common. Events B and C have common
sample points, so they are not mutually exclusive.

Suppose you roll a die two times. Is each roll of the die an independent event?
Yes. Two events are independent when the occurrence of one has no effect on the
probability of the occurrence of the other. Neither roll of the die affects the
outcome of the other roll; so each roll of the die is independent.