.m

19 We must emphasize that events are not always independent. In Example 3.19 the computers might have their power supply from the same electrical circuit, and that circuit may not be protected against electrical surges. In that case a power surge that increases the probability of failure for one computer would result in an increase for all computers Therefore, the events are not independent. The condition that the events are independent is an assumption and should be used only after careful analysis of the process that is being analyzed The following two examples illustrate how we can often simplify the determination of the probability of an event by first computing the probability of the complement and then using the probability of the complement to obtain the probability of the event of interest Example 3.20 The Birthday Problem (Complement Rule) A great question for a party is. What is the probability that at least 2 people in this room have the same birthday (month and day)? Unfortunately, it will be difficult for you to share the solution procedure at the party To make the problem manageable, we assign all those born on February 19 to March 1 and assume that all 365 possible birthdays are equally likely in the population at large. We also assume that the people in the room are a random sample, with respect to birthdays of the larger population. (These simplifications have only very smallet fects on the numerical results.) Address Links Desicop Local Dis