Suppose an influenza epidemic strikes a city. In (DGC + 1500/DGC + 10)% = _____

Question

Suppose an influenza epidemic strikes a city. In (DGC + 1500/DGC + 10)% = _____ of families the mother has influenza; in (DGC + 1500/DGC + 10)% = _____ of families the father has influenza; and in (DGC + 1000/DGC + 2)% = _____ of families both the mother and father have influenza. Let the events A_1 = {mother has influenza} and A_2 = {father has influenza}. (a) What is the conditional probability that the father has influenza given that the mother has influenza? (b) What is the conditional probability that the father has influenza given that the mother does not have influenza?

Explanation / Answer

(a) DGC = 321

so % families ,, mothes have influenza = { (DGC + 1500)/ DGC + 10) % = 15.6728%

so % families, fathers have influenza = { (DGC + 1500)/ DGC + 10) % = 15.6728%

and % families, where both parents have influenza ={DGC +1000)/DGC +2) % = 6.1152%

(a) Pr( Father have influenza if mother have influenza) P(A1/A2)= P(A1 and A2 )/ P(A2 ) = 6.1152/ 15.6728

= 0.39

(b) Pr( Father have influenza if mother have influenza) P(A1/A2') = P(A1 and A2 ')/ P(A2 ') = ( 0.156728- 0.061152)/( 1- 0.154728) = 0.113

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