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Use for question 10: A particular type of scan is used to try to determine wheth

ID: 3069430 • Letter: U

Question

Use for question 10: A particular type of scan is used to try to determine whether brain tumors are cancerous or not. Each time a tumor is scanned, the result is reported as either “positive”, “negative” or “inconclusive”. Among tumors that are cancerous, 68% of scans are “positive”, 28% of scans are “inconclusive”, and 4% of scans are “negative”. Among tumors that are NOT cancerous, 60% of scans are “negative”, 37% of scans are “inconclusive” and 3% of scans are “positive”. Historically, among all brain tumors, 67% are not cancerous.

10. If a tumor is scanned and the result is labeled as “inconclusive” what is the probability that the tumor is not cancerous?

Explanation / Answer

P(Not Cancerous | Inconclusive) = P(Inconclusive) * P(Non Cancerous) / (P(Inconclusive) * P(Non Cancerous) + P(Inconclusive) * P(Cancerous))

= 0.37*0.67/(0.37*0.67 + 0.28*0.33)

= 0.7285

Ans: 0.7285

Positive Negative Inconclusive Cancerous Tumor - Yes 0.68 0.04 0.28 Cancerous Tumor - No 0.03 0.6 0.37