The PR team at Bruno conducts their hiring process in two stages. For applicants who are classified as A, B, and G in the first stage, the chances of getting hired full-time after the second stage are...

The PR team at Bruno conducts their hiring process in two stages. For applicants who are classified as A, B, and G 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 (A, B, and G) 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 A, 39% were rated B, and the rest were rated G. If a randomly chosen applicant was rejected by three out of eight individual interviewers, what is the probability that they were rated A?