(Answered)-A researcher is developing genetic screening for a certain type - (2025 Updated Original AI-Free Solution

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Question

A researcher is developing genetic screening for a certain type of cancer. She has discovered that a certain genetic marker is associated with the cancer: 0.5% of the general population (including those with and without the genetic marker) are afflicted with this kind of cancer at some point in their lives, 0.1% of the general population have the genetic marker, and 20% of those with the genetic marker will eventually contract the disease. The researcher develops a genetic test that is 95% accurate: the chance that an individual with the marker tests positive for the marker is 95%, and the chance that an individual without the marker tests negative for the marker is 95%.Among those who will get the cancer, the fraction who also have the genetic marker is closest toa) 90%.b) 50%.c) 30%.d) 10%.e) 5%.
(Refers to the genetic screening question) The fraction of the general population (including those with and without the marker) that would be expected to test positive for the genetic marker is closest toa) 0.05%.b) 0.1%.c) 0.5%.d) 1%.e) 5%.
(Refers to the genetic screening question) Among the general population, the fraction of individuals who both have the genetic marker, and will eventually contract the cancer, is closest toa) 0.02%.b) 0.04%.c) 0.06%.d) 0.08%.e) 0.1%.
(Refers to the genetic screening question) The conditional chance that an individual selected at random from the population really has the marker, given that he or she tests positive for the marker, is closest toa) 2%.b) 20%.c) 50%.d) 70%.e) 90%.
(Refers?to?the?genetic?screening?question.Hint:P(A|B)?=(P(ABC)+P(ABC^c))/P(B))Suppose?that?whether?someone?will?eventually?contract?the?disease?is?independent?of?whether?the?genetic?test?gives?the?correct?result?(the?factors?that?affect?whether?the?test?is?accurate?for?a?given?individual?are?different?from?those?that?affect?whether?or?not?the?individual?will?contract?the?cancer).?The?conditional?chance?that?someone?will?eventually?contract?the?disease,?given?that?he?or?she?tests?positive?for?the?genetic?marker,?is?closest?toa)?1%.b)?10%.c)?30%.d)?50%.e)?90%.

Need help on Bayes Rule / Conditional Probability; I am not sure how to draw the tree diagram.