6. In an isolated housing area consisting of 70 households, the residents are al

Question

6. In an isolated housing area consisting of 70 households, the residents are allowed to have at most one dog and at most one cat per household. Currently 35 households have a dog, 12 have both a cat and a dog, and 24 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. a. The selected household has a dog but no cat, b. The selected household has a cat. c. The selected household has a cat but no dog. d. The selected household has a cat or a dog but not both

Explanation / Answer

Ans:

Total number of households=70

Given that

D=35

D and C=12

D' and C'=24

a)having dog but not cat=DC'=D-D and C=35-12=23

b)having a cat=C=70-23-24=23

C=23

c)having cat but not dog=C-D and C=23-12=11

d)having cat or dog,but not both=D+C-D and C=35+23-12=46

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