Question
In a certain Algebra 2 class of 20 students, 14 of them play basketball and 5 of them play
baseball. There are 4 students who play neither sport. What is the probability that a student
chosen randomly from the class plays both basketball and baseball?
Answer
baseball. There are 4 students who play neither sport. What is the probability that a student
chosen randomly from the class plays both basketball and baseball?
Answer
Ask by Turnbull Howell. in the United States
Mar 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that a randomly chosen student plays both basketball and baseball is
Solution
We start with the total number of students in the class, which is
The number of students who play basketball is
We are also given that
Now, solve for
The probability that a randomly chosen student plays both sports is:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To solve this, let’s first analyze the information provided. We have 20 students in total, and 4 students play neither sport. This means that 20 - 4 = 16 students play at least one sport.
There are 14 basketball players and 5 baseball players. Since we want to find the number of students who play both sports, we can use the principle of inclusion-exclusion.
Let B represent basketball players and A represent baseball players. The formula for the union of two sets is:
|B ∪ A| = |B| + |A| - |B ∩ A|
We know:
|B ∪ A| = 16 (students playing at least one sport)
|B| = 14 (basketball players)
|A| = 5 (baseball players)
|B ∪ A| = 16 (students playing at least one sport)
|B| = 14 (basketball players)
|A| = 5 (baseball players)
Plugging the values into the equation:
16 = 14 + 5 - |B ∩ A|
Now we solve for |B ∩ A| (students who play both sports):
16 = 19 - |B ∩ A|
|B ∩ A| = 19 - 16
|B ∩ A| = 3
|B ∩ A| = 19 - 16
|B ∩ A| = 3
So, there are 3 students who play both basketball and baseball.
To find the probability that a randomly chosen student plays both sports, we can use the formula:
Probability = (Number of favorable outcomes) / (Total outcomes)
The number of favorable outcomes is 3 (students playing both sports), and the total outcomes are 20 (total students in the class).
Probability = 3 / 20
Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is
