Three independent events have probabilities 1/4,1/3 and 1/2. What is the probability that exactly 1 event will occur? Solution We will need to multiply the probability of the event occurring times the probability of the events not occurring. For this we will need the complement of the probability of an event occurring which is simply P(not occurring) = 1 - P(occurring) Probability of the only the first event occurring: (1/4)(2/3)(1/2) = 1/12 Probability of the only the second event occurring: (3/4)(1/3)(1/2) = 1/8 Probability of the only the third event occurring: (3/4)(2/3)(1/2) = 1/4 Probability of only one event occurring = 1/12 + 1/8 + 1/4 = 11/24.