Chapter 1
 Lectures 1 - 3.
In this chapter we introduce the basic notions random experiment, sample space, events and probability of event.
By a random experiment, we mean an experiment which has multiple outcomes and one don't know in advance which outcome is going to occur. We call this an experiment with `random' outcome. We assume that the set of all possible outcomes of the experiment is known.
Definition 1.1. Sample space of a random experiment is the set of all possible outcomes of the random experiment.
Example 1.0.1 Toss a coin and note down the face. This is a random experiment, since there are multiple outcomes and outcome is not known before the toss, in other words, outcome occur randomly. More over, the sample space is $ \{ H, \, T \}$
Example 1.0.2 Toss two coins and note down the number of heads obtained. Here sample space is $ \{0,\, 1,\, 2\}$.
Example 1.0.3 Pick a point `at random' from the interval $ (0, \, 1]$. `At random' means there is no bias in picking any point. Sample space is $ (0, \, 1]$.