Can you please check that my answer for B) was correct as well as helping me find the equation to solve C) ?? I love that this app helps find the answers but id also like to know how to find it on my own! Thank you :)

Example - diagnostic testing 10% of prisoners in a Canadian prison are HIV positive. A test will correctly detect HIV 95% of the time, but will incorrectly "detect" HIV in non-infected prisoners 15% of the time (false positive). If a randomly selected prisoner tests positive, find the probability the prisoner is HIV+. Let: A = a prisoner is HIV positive B = a prisoner tests positive a) From the information given, construct a tree diagram. . 95 AA = . 095 - 1 SICK FNe . 05 AB = . 005 not sick . 15 9 F POS BA= . 135 . 85 BB =. 765 b) Find the probability that a prisoner tests positive. .095 . 135 23 c) Find the probability that a prisoner is HIV positive, given that he/she tests positive