Name and discuss the rules of probability.

Question

What will be an ideal response?

Answer 1

This expresses the bounding rule of probabilities—the probability of any event is bounded by 0 and 1.0. Any probability can never be less than zero or greater than 1.0. A probability of zero means that event A is impossible, probabilities close to zero imply that event A is unlikely to occur, probabilities close to 1.0 imply that there is a good chance that event A will occur, and a probability of 1.0 implies that event A will always occur.
Addition rule of probabilities: This rule is the “or” rule because it allows us to calculate the probability of one event or the other event occurring.
The restricted addition rule of probabilities states that the probability of either of two mutually exclusive events occurring is equal to the sum of their separate probabilities. In other words, if event A and event B are mutually exclusive events, then the probability of event A or B occurring, which is written P(A or B), is equal to P(A) + P(B).
When two events are not mutually exclusive, we must apply the general addition rule of probabilities. This form of the addition rule states that, for two non-mutually exclusive events, events A and B, the probability of event A or event B occurring is equal to the sum of their separate probabilities minus the probability of their joint occurrence: P(A or B) = P(A) + P(B) – P(A and B). The new part of the addition rule is the last term, P(A and B), and is the probability of event A and B occurring at the same time or simultaneously—that is, their joint probability.
The multiplication rule of probabilities is often referred to as the “and rule” because with it we can determine the probability of both one event and another (or others) occurring. The application of the multiplication rule to two events is written as P(A and B).
The restricted multiplication rule of probabilities concerns the case where the events are independent of one another. Two events are independent of each other when the occurrence of one event has no effect on the occurrence of another event. In other words, there is no relationship between independent events. If two or more events are independent, then the probability of their joint occurrence is equal to the product of their separate probabilities.
The general multiplication rule of probabilities states that the probability of two non-independent events, events A and B, occurring is equal to the probability of event A times the conditional probability of event B: P(A and B) = P(A) × P(B|A). The last term of this formula, the conditional probability, is something new and is read, “the conditional probability of event B given event A.”