It is also important to distinguish between the terms mutually exclusion and indepen dent. Two events are mutually exclusive if they cannot occur jointly; that is, the probability of their intersection is 0. For independent events the probability of their intersection is the 18 product of their individual probabilities and, in general, that probability is not 0 (unless the probability of one of the events is 0, and that result is not very interesting). Also note that if we know two events are mutually exclusive, then if one occurs, the other cannot, and the events are not independent In some circumstances independence can be deduced, or at least reasonably inferred, from the nature of a random experiment. For example, if we toss a fair coin two or more times, the probability of a head is the same for each toss and is not influenced by the out- come of the previous toss. Then the probability of the intersection can be computed from the product of individual probabilities. This is particularly useful in the case of repeated trials that are logically independent. Example 3.19 Computer Repair (Independence) The experience for a particular computer model is that 90% of the computers will oper- ate for at least one year before repair is required. A manager purchases three of these computers. What is the probability that all three will work for one year without requir- ing any repair? Sot li