In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male. Find each of the following conditional probabilities if an animal is selected at random: a) The pet is male, given that it is cat. b) The pet is a cat, given that it is female. c) The pet is female, given that it is a dog.

Answer with Step-by-step explanation:We are given that Total dogs=24 Total cats=18Total animals=24+18=42Male dogs=8Male cats=6Total male animals=8+6=14Total female animals=42-14=28Female cats=18-6=12Dogs female=24-8=16a.We have to find the probability that the pet is male, given that it is cat.It means we have to find P(Male/cat)  Conditional probability: [tex]P(A/B)=\frac{P(A\cap B)}{P(B)}[/tex]P(Cat)=[tex]\frac{18}{42}[/tex][tex]P(male cat)=\frac{6}{42}[/tex][tex]P(Male/cat)=\frac{\frac{6}{42}}{\frac{18}{42}}[/tex]P(male/cat)=[tex]\frac{6}{18}=0.33[/tex]b.[tex]P(female cat)=\frac{12}{42}[/tex][tex]P(female)=\frac{28}{42}[/tex][tex]P(Cat/Female)=\frac{\frac{12}{42}}{\frac{28}{42}}=\frac{12}{28}=0.43[/tex]c.P(Dog)=[tex]\frac{24}{42}[/tex][tex]P(dog female)=\frac{16}{42}[/tex][tex]P(female/dog)=\frac{\frac{16}{42}}{\frac{24}{42}}[/tex][tex]P(female/dog)=\frac{16}{24}=0.67[/tex]