In a certain Algebra 2 class of 27 students, 11 of them play basketball and 13 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
In a certain Algebra 2 class of 27 students, 11 of them play basketball and 13 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
To find the probability that a student chosen randomly from the class plays basketball or baseball, we need to find the total number of students who play basketball or baseball and divide it by the total number of students.
Given that there are 27 students in the class, 5 of whom play neither sport, we first need to determine the number of students who play basketball or baseball.
To do this, we can add the number of students who play basketball (11) to the number of students who play baseball (13):
11 + 13 = 24
So, there are 24 students who play either basketball or baseball.
Now, to calculate the probability, we divide the number of students who play basketball or baseball by the total number of students:
Probability = (Number of students who play basketball or baseball) / (Total number of students)
Probability = 24 / 27
Simplifying the fraction, we have:
Probability = 8 / 9
Therefore, the probability that a student chosen randomly from the class plays basketball or baseball is 8/9.
To find the probability that a student chosen randomly from the class plays basketball or baseball, we need to determine the total number of students who play basketball or baseball and divide it by the total number of students in the class.
Step 1: Find the total number of students who play basketball or baseball.
Given that there are 11 students who play basketball and 13 students who play baseball, we need to add these numbers together. However, we need to be careful not to count any students twice if they play both sports.
Step 2: Find the number of students who play both basketball and baseball.
Since we know that there are 27 students in the class, and there are 5 who play neither sport, we can subtract this number from the total number of students to find the total number of students who play basketball or baseball or both.
Total number of students who play basketball or baseball = Number of basketball players + Number of baseball players - Number of students who play both + Number of students who play neither
Step 3: Calculate the probability.
Finally, to find the probability, divide the total number of students who play basketball or baseball by the total number of students in the class.
Probability = Number of students who play basketball or baseball / Total number of students in the class
Let's calculate it:
Number of students who play basketball or baseball = 11 + 13 - (Number of students who play both) + (Number of students who play neither)
Number of students who play basketball or baseball = 11 + 13 - (Number of students who play both) + 5
Number of students who play basketball or baseball = 29 - (Number of students who play both)
Since we don't have the exact number of students who play both sports, we cannot calculate the exact probability. However, we can provide a range. The probability will be between the minimum value of 29 - 5 = 24 and the maximum value of 29.
Therefore, the probability that a student chosen randomly from the class plays basketball or baseball is between 24/27 and 29/27.
If by "basketball or baseball" you mean either or both, then clearly that is 27-5 = 22, so 22/27
If you mean ONLY basketball or baseball, but not both, then if x play both, you have
11+13-x = 27-5
x = 2
So P(exactly one sport) = 20/27