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 12.34% ). a) 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 seventh message she checks. b) Compute the probability that the first legitimate e-mail she finds is the seventh or eighth message she checks. c) Compute the probability that the first legitimate e-mail she finds is among the first seven messages she checks. 04 d) On average, how many messages should she expect to check before she finds a legitimate e-mail? (Round your answer to one decimal place.) 0 messagesWhen you post a picture on social media, it seems like your friends randomly "like" the picture. Independent of the quality or the humor of the photo, there seems to be a 29.8% chance of the picture being "liked" for any given picture. Let X represent the number of pictures you post until one is "liked." (X represents the photo number that is actually liked.) Find: X: 08 X 6 P(X=5) 4 P(X<8) 08 P(X>9) P(6X8) 0sA study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 92.6% for the medical students admitted through special programs. Be sure to enter 4 digits of accuracy for this problem! If 12 of the students from the special programs are randomly selected, find the probability that at least 11 of them graduated. P(x11)= If 12 of the students from the special programs are randomly selected, find the probability that at most 9 of them graduated. P(x9)= Would it be unusual to randomly select 12 students from the special programs and get at most 9 that graduate? yes, it is unusual no, it is not unusual.