A particular type of scan is used to try to determine whether brain tumors are c

Question

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(inconclusive) = P(cancerous and inconclusive+not cancerous and inconclusive)

= (1-0.67) x 0.28 + 0.67 x 0.37

= 0.3403

hence.

P(cancerous|inconclusive) =P(cancerous and inconclusive)/P(inconclusive)

= (1- 0.67) x 0.28/0.3403

= 0.2715

Cheers!

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