19. Solution of the event probability: the probability of the event to be solved is converted into the probability of the event with equal possibility (often using the knowledge of permutation and combination), and the probability of one of several mutually exclusive events events. Using the probability of opposite events, it is converted into the probability of simultaneous occurrence of independent events, which is regarded as the probability that an event happens exactly k times in n experiments, but attention should be paid to the use conditions of the formula.

(1) if events a and b are mutually exclusive events, then P(A+B)=P(A)+P(B).

(2) if events a and b are independent events, then p (a b) = p (a) p (b).

(3) If events A and B are opposite events, then P(A)+P(B)= 1 In general,

(4) If the probability of an event in an experiment is p, then the probability that it happens exactly k times in n independent repeated experiments: