Solve the math problem 400 students are asked if they live in an apartment and have a pet: Apartment: 120 Both: 30 Pet: 90 The probability that a randomly selected student not living in an apartment has a pet is

To find the probability that a randomly selected student not living in an apartment has a pet, you can use conditional probability. The notation for this probability is $$\( P(\text{Pet | Not Apartment}) \)$$, and it is calculated as the number of students with both a pet and not living in an apartment divided by the total number of students not living in an apartment. Given: - Students living in an apartment with a pet: 30 - Students not living in an apartment with a pet: $$\(90 - 30 = 60\)$$ (since there are 90 students with a pet and 30 of them live in an apartment) Now, calculate the probability: $$\[ P(\text{Pet | Not Apartment}) = \frac{\text{Number of students with a pet and not living in an apartment}}{\text{Total number of students not living in an apartment}} \]$$ $$\[ P(\text{Pet | Not Apartment}) = \frac{60}{400 - 120} \]$$ $$\[ P(\text{Pet | Not Apartment}) = \frac{60}{280} \]$$ Now, simplify the fraction if possible. $$ \frac{60}{280}=\frac{3}{14} $$ So, the probability that a randomly selected student not living in an apartment has a pet is $$\( \frac{3}{14} \)$$