Question

2. In an isolated housing area consisting of 50 households, the residents are allowed to have at most one dog and at most one cat per household. Currently 25 households have a dog, 7 have both a cat and a dog, and 18 have neither a cat nor a dog. An experiment consists of randomly selecting a household and observing whether that household has a cat or a dog, or both. Using D to denote the event that the selected household has a dog and C to denote the event that the selected household has a cat, symbolically denote the following events and identify the number of households represented by each

Answer 1

here from given information:

n(D) =25 (as 25 house have dogs) ; n(C n D)= 7 (as 7 have both cats and dogs)

n(C' n D') =18

as n(C u D) =50-n(C' n D')=50-18=32

a)

n(D n C^c )=n(D) -n(D n C)=25-7=18

b)

n(C) =n(C u D)+n(C n D)-P(D)=32+7-25=14

c)

n(C n D') =n(C)-n(C n D)=14-7=7

d) n(C u D)-n(C n D)=32-7=25