Question
The Venn diagram below shows the frequency of students that are taking Algebra 2 and Anatomy.
The Venn diagram shows two intersecting circles. The first circle is labeled Algebra 2 with the number 9 labeled inside. The second circle is labeled Anatomy with the number 11 labeled inside. The area where the circles overlap is labeled 15. The area outside of the circles is labeled 13.
What is the probability of choosing a student that is taking Anatomy or not taking Algebra 2?
Enter the answer in lowest terms.
(1 point)
P(taking Anatomy or not taking Algebra 2) =
$$
The Venn diagram shows two intersecting circles. The first circle is labeled Algebra 2 with the number 9 labeled inside. The second circle is labeled Anatomy with the number 11 labeled inside. The area where the circles overlap is labeled 15. The area outside of the circles is labeled 13.
What is the probability of choosing a student that is taking Anatomy or not taking Algebra 2?
Enter the answer in lowest terms.
(1 point)
P(taking Anatomy or not taking Algebra 2) =
$$
Answers
GPT-4o mini
To find the probability of choosing a student that is taking Anatomy or not taking Algebra 2, we can use the concept of total counts and the inclusion-exclusion principle.
From the information in the Venn diagram:
- Students taking only Algebra 2: 9
- Students taking only Anatomy: 11
- Students taking both subjects: 15
- Students taking neither subject: 13
First, let's calculate the total number of students:
Total students = Students only in Algebra 2 + Students only in Anatomy + Students taking both + Students taking neither
\[
= 9 + 11 + 15 + 13 = 48
\]
Next, we need to find the number of students who are either taking Anatomy or not taking Algebra 2.
1. **Students taking Anatomy**: This includes those taking only Anatomy plus those taking both subjects:
\[
\text{Students taking Anatomy} = 11 + 15 = 26
\]
2. **Students not taking Algebra 2**: This includes those taking only Anatomy, those taking both subjects, and those taking neither:
\[
\text{Students not taking Algebra 2} = 11 + 15 + 13 = 39
\]
Now we need to check for any overlap. Students who are not taking Algebra 2 are the ones taking only Anatomy (11), those taking both subjects (15), and those taking neither (13). There is no double counting here because we are looking for students not taking Algebra 2.
Using the inclusion-exclusion principle:
\[
P(\text{taking Anatomy or not taking Algebra 2}) = P(\text{taking Anatomy}) + P(\text{not taking Algebra 2}) - P(\text{taking both})
\]
We have:
- \(P(\text{taking Anatomy}) = \frac{26}{48}\)
- \(P(\text{not taking Algebra 2}) = \frac{39}{48}\)
- \(P(\text{taking both}) = \frac{15}{48}\)
Thus:
\[
P(\text{taking Anatomy or not taking Algebra 2}) = \frac{26}{48} + \frac{39}{48} - \frac{15}{48} = \frac{26 + 39 - 15}{48} = \frac{50}{48} = \frac{25}{24}
\]
However, since we exceeded 1, indicating we have a miscalculation, we need to account only for the total counts.
Thus, we can directly add the unique counts:
We know 39 students are either taking Anatomy or not taking Algebra 2.
Thus, the probability can be simplified as:
\[
P(\text{either Anatomy or not Algebra 2}) = \frac{39}{48}
\]
Reducing this fraction:
\[
\frac{39}{48} = \frac{13}{16}
\]
So, the final answer is:
\[
\boxed{\frac{13}{16}}
\]
From the information in the Venn diagram:
- Students taking only Algebra 2: 9
- Students taking only Anatomy: 11
- Students taking both subjects: 15
- Students taking neither subject: 13
First, let's calculate the total number of students:
Total students = Students only in Algebra 2 + Students only in Anatomy + Students taking both + Students taking neither
\[
= 9 + 11 + 15 + 13 = 48
\]
Next, we need to find the number of students who are either taking Anatomy or not taking Algebra 2.
1. **Students taking Anatomy**: This includes those taking only Anatomy plus those taking both subjects:
\[
\text{Students taking Anatomy} = 11 + 15 = 26
\]
2. **Students not taking Algebra 2**: This includes those taking only Anatomy, those taking both subjects, and those taking neither:
\[
\text{Students not taking Algebra 2} = 11 + 15 + 13 = 39
\]
Now we need to check for any overlap. Students who are not taking Algebra 2 are the ones taking only Anatomy (11), those taking both subjects (15), and those taking neither (13). There is no double counting here because we are looking for students not taking Algebra 2.
Using the inclusion-exclusion principle:
\[
P(\text{taking Anatomy or not taking Algebra 2}) = P(\text{taking Anatomy}) + P(\text{not taking Algebra 2}) - P(\text{taking both})
\]
We have:
- \(P(\text{taking Anatomy}) = \frac{26}{48}\)
- \(P(\text{not taking Algebra 2}) = \frac{39}{48}\)
- \(P(\text{taking both}) = \frac{15}{48}\)
Thus:
\[
P(\text{taking Anatomy or not taking Algebra 2}) = \frac{26}{48} + \frac{39}{48} - \frac{15}{48} = \frac{26 + 39 - 15}{48} = \frac{50}{48} = \frac{25}{24}
\]
However, since we exceeded 1, indicating we have a miscalculation, we need to account only for the total counts.
Thus, we can directly add the unique counts:
We know 39 students are either taking Anatomy or not taking Algebra 2.
Thus, the probability can be simplified as:
\[
P(\text{either Anatomy or not Algebra 2}) = \frac{39}{48}
\]
Reducing this fraction:
\[
\frac{39}{48} = \frac{13}{16}
\]
So, the final answer is:
\[
\boxed{\frac{13}{16}}
\]