Gymnasiematematik(high school math) Probability


The probability of a certan outcome of an experiment can be calculated as the quotient of the number of outcomes giving the desired result and the number of possible outcomes.

P(A) = (number of outcomes giving the desired results)/ (number of all  possible outcomes)
Therfore 0 < P(A) < 1 with 0 being the probability for an impossible outcome and 1 the probability for a certain outcome.
A multi-step experiment can be illustrated with a tree-diagram.
Two outcomes are complementary if either of them most occur if the other doesn’t.
The sum of their probabilities must be one.

Event Probability
A                P(A)
not A        CP(A) = 1- P(A) The complement to A
A or B      P(A U B)= P(A) + P(B) for mutually exclusive events otherwise

P(A U B)= P(A) + P(B) – P(A ∩ B) The union of A and B i.e. the occurence of either of them.

A and B   P(A ∩ B) The occutence of both of them at the same time can be found by multplying the individual probabilities: P(A)*P(B)*P(C)*…….. *P(Z).
A given B P(A¦B) =P(A ∩ B)/P(B)  this gives the probability for A given that B has already happened.