The significance of 1. event sum

Event a and event b can be added. A+B represents such an event: under the same experiment, at least one of A or B represents occurrence. For example, throw a cube toy with the numbers 1, 2, 3, 4, 5 and 6 on its six sides. If odd points are thrown, record it as event A; If the number of throwing points is not greater than 3, it is recorded as event B, and event A+B indicates that the number of throwing points is one of 1, 2, 3 and 5.

The event "A 1+A2+…+An" indicates such an event. In the same experiment, at least one of A 1, A2, …, an happened, which means it happened.

2. The significance of mutually exclusive events

An event that cannot happen at the same time is called mutually exclusive events. For example, draw a card from 52 playing cards. Let event A draw a red heart and event B draw a red square. Events a and b are mutually exclusive.

3. mutually exclusive events's probability addition formula.

If events a and b are mutually exclusive, then:

P(A+B)=P(A)+(B)

summary

The two events A and B are mutually exclusive, and the probability addition formula can be applied:

P(A+B)=P(A)+P(B)，

This formula can also be extended to n cases of mutual mutually exclusive events:

P(a 1+A2+…+An)= P(a 1)+P(A2)+…+P(An).

If two events A and B are not mutually exclusive, then there is a probability addition formula.

P(A+B)=P(A)+P(B)-P(AB).

Probability multiplication formula

Conditional probability: if the probability of event A is calculated under the condition that event B has occurred, this probability is called the conditional probability of event A under the condition that event B has occurred, and it is recorded as P(A|B). The calculation formula is as follows:

P(A|B)=P(A | B)/P(B)

Multiplication theorem: the probability of the product of two events is equal to the product of the probability of the next event and the conditional probability of another event, that is, P(AB)=P(A)P(B|A)=P(B)P(A|B).

Independent events: If the occurrence of any event does not affect the probability of the other event, the two events are said to be independent of each other, that is, P(B|A)=P(B) or P(A|B)=P(A), then A and B are independent.

It can also be defined as follows: If the probability of the product event of two events A and B is equal to the product of these two events, two events A and B are said to be independent of each other, that is, P(AB)=P(A)P(B), then A and B are independent.