An applicant for a faculty position at a certain university is told by the department chair that she has a 0.95 probability of being invited for an interview. Once invited for an interview, the applicant must make a presentation and win the votes of a majority (at least 8) of the department's 14 current members. From previous meetings with four of these members, the candidate believes that three of them would certainly vote for her while one would not. She also feels that any member she has not yet met has a 0.50 probability of voting for her. Department members are expected to vote independently and with no prior consultation. What are the candidate's chances of getting the position?
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