The HR team at Nielsen conducts their hiring process in two stages. For applicants who are classified as Alpha, Beta, and Gamma in the first stage, the chances of getting hired full-time after the...

The HR team at Nielsen conducts their hiring process in two stages. For applicants who are classified as Alpha, Beta, and Gamma in the first stage, the chances of getting hired full-time after the second stage are 74%, 43% and 26% respectively. If an applicant is not hired full-time, they are either put on a probation list, or rejected. Unselected applicants of all categories (Alpha, Beta, and Gamma) are half as likely to be put on the probation list as being rejected. During the first stage of the most recent hiring, 22% of the applicants were rated Alpha, 39% were rated Beta, and the rest were rated Gamma. If a randomly chosen applicant was rejected by three out of eight individual interviewers, what is the probability that they were rated Alpha?