Sample Space | Probability Theory
SAMPLE SPACE
Sample space can be either discrete or continuous depending on the type of random experiment.
- Discrete sample space
- Continuous sample space
A sample space is a collection of all possible outcomes of a random experiment. A sample space may be finite or infinite. Also, a sample space may be discrete or continuous.
Understanding numerical data as shown in below table will help to understand discrete and continuous sample spaces.
Discrete Sample Space
Example 1:
Tossing a coin (object with two distinct sides) is an example of discrete sample space. Generally, a discrete sample space does not contain decimal values. In the case of a single toss, the sample space has two elements: {Head, Tail}, or {H, T}, or {0, 1}.
Suppose a fair coin is tossed 3 times and counted for number of heads. Note that sample space does not contain 2.5 head or 1.6 tails. So, when doing a coin experiment, we cannot have 2.5 heads or 1.6 tails. The sample space obtained from experiments like this is known as discrete sample space.
Example 2:
Rolling a die – A common die is a small cube whose faces shows numbers 1, 2, 3, 4, 5, 6.
Continuous Sample Space
Example1:
Human height. The experiment is to randomly select a human and measure his or her length.
Sample space can be any value within a segment, say [40, 270] centimetres. Note that human population is a discrete sample space.
S= {Heights of 6 billion humans inhabiting the planet Earth}
Example2:
Chord (line joining the ends of an arc) length: Given a circle of radius R, the experiment is to randomly select a chord in that circle.
S = {AB: A and B are points on a given circle}
