SOLUTION: Of all the people applying for a certain​ job, 80​% are qualified and 20​% are not. The personnel manager claims that she approves qualified people 75​% of

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Question 1027303: Of all the people applying for a certain​ job, 80​% are qualified and 20​% are not. The personnel manager claims that she approves qualified people 75​% of the​ time; she approves unqualified people 20​% of the time. Find the probability that a person is qualified if he or she was approved by the manager.
I did a tree diagram and multiplied .80 Q x .75 = .60 . However I don't think this is right way to do it.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at the four possible outcomes,
Qualified, approved
Qualified, not approved
Not qualified, approved
Not qualified, not approved
P%28QA%29=0.8%280.75%29=0.6
P%28QN%29=0.8%280.25%29=0.2
P%28NA%29=0.2%280.2%29=0.04
P%28NN%29=0.2%280.8%29=0.16
Since these are the only four outcomes the probabilities must sum to 1. You can verify that this is the case.
Yes, P%28QA%29=0.6