Question

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

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Eliseo

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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 \( \frac{3}{14} \)

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