Introduction to Probability- Part 1

This will contain introduction to probability for undergraduate or graduate level students.

Probability Space

Probability space is defined by a tuple consisting of three elements i.e. ($\Omega$, $\mathbf{F}$, $\mathbf{P}$) wherein $\Omega$ refers to the sample space, $\mathbf{F}$ refers to the event space or sigma algebra and $\mathbf{P}$ is the probability measure.

• Sample Space: A set consisting of all the possible outcomes of a random experiment. Ex: If the random experiment is the roll of a dice, the sample space is {1, 2, 3, 4, 5, 6} whereas if the experiment if the toss of a coin, the sample space is {H, T}.
• Event Space: A subset of the power set of sample space which satisfies the following conditions i.e. the event space is closed under complements, closed under countable unions and contains the sample space.
• Probability Measure: