Rules of probability distributions

 Here are some simple explanations and examples of the rules of probability distributions:

The sum of the probabilities of all possible outcomes must be equal to 1. This means that if you add up all the chances of something happening, it should equal 100%. For example, if you flip a coin, there is a 50% chance of getting heads and a 50% chance of getting tails. If you add these probabilities together, you get 100%.

The probability of each outcome must be between 0 and 1. This means that the chance of something happening cannot be less than 0% or more than 100%. For example, if you roll a die, the chance of rolling a 3 is 1/6, or about 17%. This probability is between 0 and 1.

The probability of an event occurring is equal to 1 minus the probability of it not occurring. For example, if the probability of it raining tomorrow is 50%, the probability of it not raining tomorrow is 50%.

The probability of the union of two disjoint events is equal to the sum of the probabilities of the individual events. Disjoint events are events that cannot happen at the same time, such as picking a red ball or a blue ball from a bag of balls. If the probability of picking a red ball is 1/3 and the probability of picking a blue ball is 1/3, the probability of picking either a red ball or a blue ball is 2/3.

The probability of the intersection of two independent events is equal to the product of the probabilities of the individual events. Independent events are events that have no effect on each other, such as flipping two coins and getting heads on both. If the probability of flipping a coin and getting heads is 1/2 and the probability of flipping another coin and getting heads is also 1/2, the probability of flipping two coins and getting heads on both is 1/4.