# Introduction to Probability Notes

What is Probability?
Probability theory is the branch of mathematics that studies the possible outcomes of given events together with the outcomes’ relative likelihoods and distributions. In common usage, the word “probability” is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty). Factually, It is the study of random or indeterministic experiments eg tossing a coin or rolling a die. If we roll a die, we are certain it will come down but we are uncertain which face will show up. Ie the face showing up is indeterministic. Probability is a way of summarizing the uncertainty of statements or events. It gives a numerical measure for the degree of certainty (or degree of uncertainty) of the occurrence of an event.
We often use P to represent a probability Eg P(rain) would be the probability that it rains. In other cases Pr(.) is used instead of just P(.).

Definitions

• Experiment: A process by which an observation or measurement is obtained. Eg tossing a coin or rolling a die.
• Outcome: Possible result of a random experiment. Eg a 6 when a die is rolled once or a head when a coin is tossed.
• Sample space: Also called the probability space and it is a collection or set of all possible outcomes of a random experiment. Sample space is usually denoted by S or
or U
• Event: it’s a subset of the sample space. Events are usually denoted by upper case letters.

Approaches to Probability
There are three ways to define probability, namely classical, empirical and subjective probability.

1 Classical probability
Classical or theoretical probability is used when each outcome in a sample space is equally likely to occur. The underlying idea behind this view of probability is symmetry. Ie if the sample space contains n outcomes that are fairly likely then P(one outcome)=1/n……………………………………………………………..

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