8. Use the Venn Diagram below to find the probability that event D occurs given

Question

8. Use the Venn Diagram below to find the probability that event D occurs given that event C does not occur. 0.4 1) 0.10.3 0.2 9. Based on the Venn Diagram below, which of the following statements are true? a) b) c) TRUE OR FALSE: E and F are independent TRUE OR FALSE: E and F are mutually exclusive TRUE OR FALSE: E and F are exhaustive 0.70 0.20 0.10 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 cancerous?

Explanation / Answer

8) here P(Cc) =1-0.1-0.3 =0.6

hence probability that D occur given C does not =P(D|Cc) =P(DnCc)/P(Cc) =0.2/0.6 =1/3 =0.3333

9)

a)false asP(EnF)=0 and not equal to P(E)*P(F)

b) true as P(EnF) =0

c) false as P(E)+P(F) is not equal to 0.

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

=(1-0.67)*0.28+0.67*0.37=0.3403

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

=(1-0.67)*0.28/0.3403 =0.2715

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