Sample Space

Sample space is a list of all possible outcomes of a random experiment. It is denoted by “S”.  Each single possible outcome in a sample space is known as element of the sample space. When sample space contains finite number of outcomes then it is known as finite or discrete sample space.

Sample Space Solved Examples

Example 1:

Statement:

A person has selected two bulbs randomly from a lot. Prepare it sample space.

Solution:

First calculate the total number of outcomes

Total outcomes = 2^2 = 4

These four outcomes can be counted as;

• Both bulbs are good
• First bulb is good & second is defective one
• First bulb is defective & second is good
• Both bulbs are defective

In expression form, it can be written as;

S= {(GG),(GD),(DG),(DD)}

Where;

G = good bulbs

D = defective bulbs

That sample space is discrete sample space, because a single selected bulb cannot be count as half is defective and remaining half is good or 25% is good and rest is defective. In simple words, it is impossible to form a sample space for continuous data. For example if you want to measure the temperature between 35⁰C & 36⁰C, then sample space is not possible. This is so because there are number of possible outcomes.

Example 2:

Two coins are tossed. Prepare the sample space.

Solution:

When coins are tossed then the possible outcomes are;

• Both are head
• Head on first and tail on the second coin
• Tail on first and head on the second
• Both are tail

Sample space = S = {HH, HT, TH, TT}

Where;