could you help me solve this : Conditioning on a household is affected by this virus, what is the probability that this household has a pet?

Question

virus is spreading in a city. 6% of households who have pets will be affected, while 1% of households without pets will be affected. In this city, about 20% of the households have pets and 80% don't. Conditioning on a household is affected by this virus, what is the probability that this household has a pet?

Answer 1

We should formulate the problem to be able to attain the answer: $$\Pr(\text{Being affected}|\text{Having pets})=6\%\\\Pr(\text{Being affected}|\text{Not having pets})=1\%\\\Pr(\text{Having pets})=20\%\\$$Then we are looking for$$\Pr(\text{Having pets}|\text{Being affected})$$which using Bayes's theorem can be calculated as$$\Pr(\text{Having pets}|\text{Being affected})\\=\\{\Pr(\text{Having pets})\Pr(\text{Being affected}|\text{Having pets})\over\Pr(\text{Having pets})\Pr(\text{Being affected}|\text{Having pets})+\Pr(\text{Not having pets})\Pr(\text{Being affected}|\text{Not having pets})}\\=\\{20\%\times 6\%\over 20\%\times 6\%+80\%\times 1\%}=60\%$$