Mastering Probability Rules: Addition, Multiplication, Complement, Conditional And Bayes’ Theorem

probability rules

All legitimate assignments of probability, whether based on data or personal obey the same

There are various probability rules that are used for predicting the likelihood of an event occurring. Some of the most common probability rules include:

1. Addition Rule: The addition rule is used when we have two or more events with no common outcomes, and we want to find the probability of either event happening. The rule states that the probability of either of the two events occurring is equal to the sum of their individual probabilities minus their joint probability, which is the probability of both events occurring.

P(A or B) = P(A) + P(B) – P(A and B)

2. Multiplication Rule: The multiplication rule is used when we have two or more events with common outcomes, and we want to find the probability of all the events occurring. The rule states that the probability of all the events occurring together is equal to the product of their individual probabilities.

P(A and B) = P(A) * P(B|A)

where P(B|A) represents the conditional probability of event B occurring given that event A has occurred.

3. Complement Rule: The complement rule states that the probability of an event not occurring is equal to one minus the probability of the event occurring.

P(A’) = 1 – P(A)

4. Conditional Probability Rule: The conditional probability rule is used to calculate the probability of an event, given that another event has occurred. The rule states that the probability of event A given event B is equal to the probability of A and B occurring divided by the probability of B occurring.

P(A|B) = P(A and B) / P(B)

5. Bayes’ Theorem: Bayes’ theorem allows us to update our original probability estimates based on new information. It is particularly useful when we want to find the probability of an event, given that we have observed another event occur. It states that the probability of event A given event B is equal to the probability of B given A, multiplied by the prior probability of A, divided by the prior probability of B.

P(A|B) = P(B|A) * P(A) / P(B)

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