Sample Space#

A lot of this material is inspired by:

  1. Wiki article

  2. Khan academy videos

  3. MIT OCW course

Assume you toss a coin once, the coin can land either as heads or tails. The outcome is unknown before the throw.

Sample Space

The sample space is the possible outcomes of the experiment. For the coin toss experiment, we can denote the sample space as: \(\Omega = \{H, T\}\)

Now,let us consider a slightly advanced example. Our experiment is to roll two die (6-faced die) and note the sum of the numbers on the top side.

The sample space for this example is:

\[\begin{split} \begin{align*} S = \{&(1, 1), (1, 2), \dots, (1, 6), \\ &(2, 1), (2, 2), \dots, (2, 6), \\ &\cdots, \cdots, \cdots, \cdots \\ &(6, 1), (6, 2), \dots, (6, 6) \} \end{align*} \end{split}\]