Rules of Probability

The probability of any event must be greater than or equal to zero and less than or equal to one. For example, the probability of tossing heads is 0.5, or the probability of rain might be 0.3.

The sum of probabilities for all possible outcomes of an event is always 1. For instance, the probability of getting heads (0.5) plus tails (0.5) equals 1. Similarly, winning a basketball game (0.7) plus losing (0.3) equals 1.

The probability that an event does not occur is 1 minus the probability of it actually occurring. For example, the probability of not rolling a 1 on a six-sided die is 1 minus the probability of rolling a 1. The probability of not raining is 1 minus the probability of rain.

Events are non-disjoint if they can happen together (e.g., a card being both a nine and a club). Disjoint events cannot happen at the same time (e.g., a coin being both heads and tails).

When events are disjoint, the probability of getting event A or event B is simply the sum of their individual probabilities. For example, the probability of drawing a six of clubs or a ten of diamonds from a deck is calculated by adding their individual probabilities.

When events are non-disjoint, the probability of A or B occurring is the sum of their individual probabilities minus the probability of them happening at the same time. For instance, the probability of drawing a six or a club is the probability of a six plus the probability of a club, minus the probability of drawing a six of clubs (the overlap).