FASTPlaqueTB is a diagnostic test for the presence of tuberculosis bacilli. In a community, for those subjects known to have the tuberculosis bacilli, the FASTPlaqueTB test was positive 70% of the time. For those subjects known not to have the tuberculosis bacilli, the FASTPlaqueTB test was negative 99% of the time. Statistics indicate that about 14.2% of the people in the community have the tuberculosis bacilli. Define all the events, draw a tree diagram, and answer the following two questions. (a). What is the probability that a randomly selected person from the community will have a positive FASTPlaqueTB test result? (b). What is the probability that a person from the community who tests positive does not have tuberculosis bacilli?

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FASTPlaqueTB is a diagnostic test for the presence of tuberculosis bacilli. In a community, for those
subjects known to have the tuberculosis bacilli, the FASTPlaqueTB test was positive 70% of the time. For
those subjects known not to have the tuberculosis bacilli, the FASTPlaqueTB test was negative 99% of the
time. Statistics indicate that about 14.2% of the people in the community have the tuberculosis bacilli.
Define all the events, draw a tree diagram, and answer the following two questions. 

 


(a). What is the probability that a randomly selected person from the community will have a positive
FASTPlaqueTB test result?

 

 

(b). What is the probability that a person from the community who tests positive does not have tuberculosis
bacilli?

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