Answer: [tex]\dfrac{2}{5}[/tex]
Step-by-step explanation:
Given : The proportion of students have a dog : [tex]P(D)=\dfrac{45}{100}[/tex]
The proportion of students have a cat : [tex]P(C)=\dfrac{30}{100}[/tex]
The proportion of students have both a dog and a cat : [tex]P(C\cap D)=\dfrac{18}{100}[/tex]
Now, the conditional probability that a student who has a dog also has a cat will be :-
[tex]P(C|D)=\dfrac{P(C\cap D)}{P(D)}\\\\\\\Rightarrow\ P(C|D)=\dfrac{\dfrac{18}{100}}{\dfrac{45}{100}}\\\\\\\Rightarrow\ P(C|D)=\dfrac{18}{45}=\dfrac{2}{5}[/tex]
Hence, the probability that a student who has a dog also has a cat = [tex]\dfrac{2}{5}[/tex]
