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In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 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 both basketball and baseball?

2 Answers

2 votes

Final answer:

To find the probability that a randomly chosen student from the class plays both basketball and baseball, we use the inclusion-exclusion principle and determine that 2 out of 13 students play both.

Step-by-step explanation:

The question asks for the probability that a student chosen randomly from the Algebra 2 class plays both basketball and baseball. We are told that the class has 26 students, 18 play basketball, 7 play baseball, and 5 play neither. To find the number of students who play both sports, we can use the principle of inclusion-exclusion. Adding the number who play basketball and baseball, we get 18 + 7 = 25. However, since the number of students is 26 and 5 play neither, we subtract those who play neither to get 26 - 5 = 21 students who play at least one of the sports. From the total of 25 (18 + 7) who seem to play basketball or baseball, we subtract the actual number who play at least one sport to find the number who play both: 25 - 21 = 4 students play both. Therefore, the probability that a randomly chosen student plays both is 4/26, which can be simplified to 2/13.

User Pablo Urquiza
by
7.8k points
5 votes

a=18−x

b=7−x

x+5+b+a=26

18−x+7−x+x+5=26

x=4

p

theprobabillty=4÷26

User Mukesh Garg
by
7.1k points