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In a certain Algebra 2 class of 29 students, 13 of them play basketball and 14 of them play baseball. There are
10 students who play neither sport. What is the probability that a student chosen randomly from the class
plays both basketball and baseball?



Answer :

Intriguing456

Answer:

[tex]P(\text{both}) = \dfrac{8}{29}[/tex]

Step-by-step explanation:

We are given the following information:

  • the class has 29 students total
  • 13 play basketball
  • 14 play baseball
  • there is overlap
  • 10 play neither sport

First, we can find the number of students who play at least one sport by subtracting the students who play neither from the total:

29 - 10 = 19

This includes the overlap (students who play both sports). Next, we can find the overlap by subtracting the number of students who play sports from the number that play basketball and baseball, separately:

(13 + 14) - 19 = 27 - 19 = 8

So, we know that 8 students play both basketball and baseball.

Finally, we can find the probability of randomly selecting a student from that plays both sports by dividing the number of students who plays both by the total number of students:

[tex]\boxed{P(\text{both}) = \dfrac{8}{29}}[/tex]

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