What is properties of probabilities?

1. Probabilities are always between 0 and 1: A probability of 0 means an event is impossible to occur, while a probability of 1 means the event is certain to occur.

2. Probabilities are additive: The probability of the occurrence of multiple events is the sum of the probabilities of all those events occurring.

3. Probabilities can be mutually exclusive or not: If two events cannot occur at the same time, they are said to be mutually exclusive. The probability of at least one of those events occurring is the sum of their individual probabilities. If two events can occur together, they are said to be non-mutually exclusive.

4. Probabilities can be conditioned: The probability of an event occurring can be modified by additional information about the circumstances in which it may occur. This is known as the conditional probability.

5. Probabilities can be independent or dependent: If the probability of one event occurring is not affected by the occurrence of another event, they are said to be independent. If the occurrence of one event affects the probability of another event, they are said to be dependent.

6. Probabilities can be manipulated using rules of probability: There are several rules of probability, including the product rule, sum rule, and Bayes' theorem, which can be used to calculate the probability of different events.

7. Probabilities can still be estimated even with incomplete information: If all information is not available, we may have to use our best judgement to estimate the probability of the event occurring.