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;

H = Head

T = Tail