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What are the rules of probability theory?

幫考網(wǎng)校2020-11-26 16:22:23

1. Probability values range from 0 to 1: The probability of an event occurring is always between 0 and 1, where 0 means that the event will not occur and 1 means that the event is certain to occur.

2. The sum of all probabilities is 1: The probabilities of all possible outcomes of an event must add up to 1.

3. The complement rule: The probability of an event not occurring is equal to 1 minus the probability of the event occurring.

4. The addition rule: The probability of either of two mutually exclusive events occurring is equal to the sum of their individual probabilities.

5. The multiplication rule: The probability of two independent events occurring together is equal to the product of their individual probabilities.

6. Conditional probability: The probability of an event occurring given that another event has already occurred is equal to the probability of both events occurring divided by the probability of the second event occurring.

7. Bayes' theorem: This theorem allows us to update our probabilities when new information becomes available. It states that the probability of an event occurring given some prior knowledge is equal to the probability of the prior knowledge given the event multiplied by the probability of the event divided by the probability of the prior knowledge.