If two events, A and B, are not mutually exclusive, then the probabilitythat either A or B occurs is the sum of their probabilities decreased by the probability of both occurring.
P(A or B)=p(A)+p(B)p(A and B)
Of 30 boys, 12 are on the Honor Roll, 10 play sports, and 15 are on the Honor Roll and play sport. What is the probability that a randomly selected student plays sports or is on the Honor Roll?
Since some students play varsity sports and are on the Honor Roll, the events are
not mutually exclusive.
p(sport or Honor Roll)

=

p(sport)+p(Honor Roll)p(sport and Honor Roll)


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