An event in which AB is a product means that event A occurs and event B occurs. As a probability and statistics problem, it is equivalent to the intersection of sets.

Theorem: Let A and B be mutually incompatible events (AB=φ), then:

P(A∪B)=P(A)+P(B)

Inference 1: If A 1, A2, …, An are incompatible with each other, then: P (A1+A2+...+An) = P (A1)+P (A2)+…+P (An).

Inference 2: Let A 1, A2, ..., A form a complete event group, then: P (A1+A2+...+An) =1.

Inference 3:? Contrary to event a.

Inference 4: if b contains a, then P (B-A) = P (B)-P (A).

Inference 5 (generalized addition formula):

For any two events a and b, there is P (A ∪ B) = P (A)+P (B)-P (AB).

Extended data:

Suppose: If events A 1, A2, …, An are incompatible with each other, and A 1+A2+…+an = ω, then A 1, A2, …, an constitutes a complete event group.

The form of total probability formula is as follows:?

The above formula is called the total probability formula.

Probability has the following seven different attributes:

Attribute1:p (φ) = 0;

Property 2: (limited additivity) When n events A 1, …, An are incompatible with each other: p (a1∧ ... ∪ an) = p (a1)+...+p (an);

Property 3: For any event, a: p (a) = 1-p (not a);

Property 4: When events A and B satisfy that A is included in B: P(B-A)=P(B)-P(A), p (a) ≤ p (b);

Property 5: For any event A, p (a) ≤1;

Property 6: For any two events A and B, p (b-a) = p (b)-p (a ∩ b);

Property 7: (addition formula) For any two events A and B, P(A∪B)= P(A)+P(B)-P(A∪B).

References:

Baidu encyclopedia-probability calculation