Answer with Step-by-step explanation:
We are given that
Total dogs=24
Total cats=18
Total animals=24+18=42
Male dogs=8
Male cats=6
Total male animals=8+6=14
Total female animals=42-14=28
Female cats=18-6=12
Dogs female=24-8=16
a.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]
