Q:

At Central Online High School, 4510045100 of the students have a dog, 3010030100 have a cat, and 1810018100 have both a dog and a cat. What is the probability that a student who has a dog also has a cat? Enter your answer as a reduced fraction with the / symbol, like this: 3/14

Accepted Solution

A:
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]