In a certain Algebra 2 class of 28 students, 23 of them play basketball and 12 of them play baseball. There are 3 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
\text{Probability: }\frac{10}{28}\text{ or }\frac{5}{14}
Probability:
10/28
or
5/14
(23 / 28) * (12 / 28) = ?
To find the probability that a student plays both basketball and baseball, we first need to determine the number of students who play both sports.
Let's denote the number of students who play both basketball and baseball as "x."
According to the information given, there are 23 students who play basketball and 12 students who play baseball. We can represent this information using a Venn diagram:
Basketball (23)
_______________
| |
x | |
| |
| |
| |
| |
|_______________|
Baseball (12)
We also know that there are 3 students who play neither sport. We can represent this information by placing the number 3 outside the circles.
Basketball (23)
_______________
| |
x | |
| |
| |
| |
| |
|_______________|
_______
3 |_______|
Now, we can use the principle of inclusion-exclusion to find the value of "x."
The total number of students in the class is 28 (given in the question).
So, by the principle of inclusion-exclusion, we can calculate "x" as follows:
Total students = Basketball + Baseball - (Basketball ∩ Baseball) + Neither
28 = 23 + 12 - x + 3
Simplifying the equation:
28 = 38 - x
Rearranging the equation to isolate "x":
x = 38 - 28
x = 10
Now that we know "x" (the number of students who play both basketball and baseball), we can calculate the probability of choosing a student who plays both sports.
Probability = Number of favorable outcomes / Total outcomes
In this case, the favorable outcome is choosing a student who plays both basketball and baseball, and the total outcomes are choosing a student randomly from the class (which is 28).
Therefore, the probability is:
Probability = x / Total students
= 10 / 28
= 5 / 14
So, the probability that a student chosen randomly from the class plays both basketball and baseball is 5/14.
To find the probability that a student chosen randomly from the class plays both basketball and baseball, we need to determine the number of students who play both sports and then divide it by the total number of students.
Let's start by finding the number of students who play both sports.
We know that there are 28 students in total, 23 of whom play basketball and 12 of whom play baseball. However, we also know that 3 students play neither sport. This means that the number of students who play at least one of the sports is the sum of those who play basketball and those who play baseball.
The number of students who play at least one sport = 23 (basketball players) + 12 (baseball players) - 3 (neither sport) = 32.
Now, we subtract the number of students who play at least one of the sports from the total number of students to find the number of students who play both sports.
Number of students who play both sports = Total number of students - Number of students who play at least one sport = 28 - 32 = -4
Wait a minute. We got a negative number for the number of students who play both sports, which doesn't make sense. It appears that there might be a mistake or inconsistency in the information provided, as there cannot be a negative number of students playing both basketball and baseball.
Please double-check the given information or provide any additional details if available.