According to Internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while the remaining 10% are legitimate. A system administrator wishes to see if the same percentages hold true for the e-mail traffic on her servers. She randomly selects e-mail messages and checks to see whether or not each one is legitimate. (Unless otherwise specified, round all probabilities below to four decimal places; i. e. your answer should look like 0.1234, not 0.1234444 or 12.34%.) Assuming that 90% of the messages on these servers are also spam, compute the probability that the first legitimate e-mail she finds is the fourth message she checks: Compute the probability that the first legitimate e-mail she finds is the fourth or fifth message she checks: Compute the probability that the first legitimate e-mail she finds is among the first four messages she checks: On average, how many messages should she expect to check before she finds a legitimate e-mail?