Probability theory fundamentals

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Probability theory is a branch of mathematics that deals with the analysis of random phenomena. It’s used to model and predict the likelihood of different outcomes in a wide variety of situations, from games of chance to the behavior of subatomic particles.

Some of the key concepts in probability theory include:

1. Sample space: This is the set of all possible outcomes of a random event. For example, in a coin toss, the sample space would be the set {of heads, tails}.
2. Probability: This is a measure of the likelihood of an outcome occurring. Probability is always a number between 0 and 1, where 0 indicates that an outcome is impossible and 1 indicates that an outcome is certain.
3. Independence: This refers to the idea that the outcome of one event does not affect the outcome of another event. For example, the outcome of a coin toss is independent of the outcome of a dice roll.
4. Complementary events: These are events that cannot both occur at the same time. For example, in a coin toss, the event “heads” is complementary to the event “tails”.
5. Additive rule: This states that the probability of two events occurring together is the sum of the probabilities of each event occurring separately. For example, the probability of flipping a coin and rolling a die and getting heads…