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In a certain Algebra 2 class of 28 students, 9 of them play basketball and 17 of them play baseball. There are 6 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Sagot :

Answer:

4/28 (simplified to 1/7)

Step-by-step explanation:

Given:

  • There are 28 total students in the class
  • 9 of them play basketball
  • 17 of them play baseball
  • 6 of them play neither sport

Question:

What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Answer:

  • Because we know there are 28 total students in the class and 6 play neither basketball nor baseball, then there are 28-6 = 22 students who either play ONLY basketball, ONLY baseball, or both
  • We know that 9 out of the 22 play basketball and 17 out of the 22 play baseball
  • Therefore, 22-9 = 13 students play ONLY basketball, and 22-17 = 5 students play ONLY baseball
  • This means that the amount of students that play BOTH basketball and baseball is 22-(13+5) = 22-18 = 4 students
  • Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is 4/28 or 1/7
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