Explain the procedure of assigning probability in the discrete world of probability theory.

In the discrete world of probability theory, the procedure of assigning probability is a fundamental process that involves several logical and mathematical steps to ensure that probabilities are defined consistently, objectively (in some cases), or subjectively (in others), depending on the context. Discrete probability theory deals with experiments that have a finite or countably infinite number of possible outcomes. Assigning probabilities in this framework involves defining a sample space, determining events, and applying axioms and rules of probability.

1. Defining the Sample Space (Ω)

The first step in assigning probabilities is to clearly define the sample space. The sample space, denoted by Ω (omega), is the set of all possible outcomes of a random experiment. Since we are dealing with the discrete case, Ω is either finite or countably infinite.

For example:

• Tossing a coin once: Ω = {Heads, Tails}

• Rolling a die: Ω = {1, 2, 3, 4, 5, 6}

• Selecting a card from a standard deck (without considering suit): Ω = {1, 2, ..., 13}

2. Defining Events

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