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Cysts ​ After Researching Cysts of a Particular Type,a Doctor

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Cysts
​ After researching cysts of a particular type,a doctor learns that out of 10,000 such cysts examined,1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient. ​ ​
-{Cysts Narrative} What is the probability that the patient has a benign tumor if he or she tests positive?


Definitions:

Organic Reaction

A chemical reaction involving organic compounds, where participants experience changes in their molecular structure.

Dienophile

A compound that participates in Diels-Alder reactions by combining with a diene to form a ring structure.

Thermal Cycloaddition

A chemical process where two or more molecules join together in a reaction that involves the redistribution of electrons and is facilitated by heat.

Allyl Anion

A negatively charged species derived from an allyl group, featuring a conjugated system of electrons across three carbon atoms.

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