table of Contents
Independent and mutually exclusive events
Definitions : each independently is set A, B are two events, If equation is met
- \ (P (AB) = P (A) P (B) \) , an event called \ (A, B \) independently of one another, referred to as \ (A, B \) independently.
- \(P(A|B)=P(A)P(B)\)
theorem:
- \ (\ Emptyset, and \ Omega with any independent events A \)
- If \ (A and B are independent, then \ overline {A} and B, A and \ overline {B}, \ overline {A} and \ overline {B} \) independently
- If \ (P (A) = 0 or 1, that P (A) independently of one another with any events \)
the difference
- Independent: two probabilities independently of each other
- Mutually exclusive: two probabilities do not occur simultaneously , there is no intersection
Independent and mutually exclusive can not simultaneously set up
- If \ (A, B \) is independently: \ (P (AB) = P (A) P (B) \)
If \ (A, B \) mutually exclusive, the \ (P (AB) = 0 \)