Events and Sample Space

Suppose an experiment that involves tossing a coin. Now, there are only two outcomes of a coin toss – Heads or Tails. The interest is to study and calculate the chances of getting a tail as a result of a coin toss. This is called a random experiment and all the possible outcomes of this experiment constitute sample space. For example, let’s say a coin is tossed 2 times. What are the possible outcomes? 

TH, HH, HT, TT

All these outcomes constitute sample space. 

Random Experiment: A random experiment is an experiment in which outcomes are random and thus cannot be predicted with certainty. 

Sample Space: Sample space is the set of all possible outcomes associated with a random experiment. It is denoted using the symbol S.  

Let’s measure the probability of getting two heads in the above experiment. Then the probability of this outcome is defined as, 

P = \frac{\text{Number of favourable Outcomes}}{\text{Total number of possible outcomes}}

For this case, favorable outcome is HH and the total number of possible outcomes are four. 

So, Probability(Getting two heads) = \frac{1}{4}

Hearing the word probability brings up nebulous concepts related to uncertainty or randomness. The concept of probability is hard to describe formally, the closest intuition is that it helps us analyze the likelihood or chances that a certain event will happen. This analysis helps us to describe a lot of phenomena we see in real life. Even the most randomly seeming processes or phenomena can be described using the probability models and can be predicted up to a certain extent. That’s why probability makes the foundation for artificial intelligence algorithms that we encounter in real life. Before formally describing probability laws, let’s look at basic terminology.