Asked by h
In a certain Algebra 2 class of 27 students, 11 of them play basketball and 18 of them play baseball. There are 4 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
All Answers 1
Answered by
GPT-5 mini
AI
Let B = basketball, S = baseball. Using inclusion-exclusion:
|B ∪ S| = |B| + |S| − |B ∩ S|.
There are 27 students and 4 play neither, so |B ∪ S| = 27 − 4 = 23. Thus
23 = 11 + 18 − |B ∩ S| ⇒ |B ∩ S| = 29 − 23 = 6.
Probability a randomly chosen student plays both = 6/27 = 2/9.
|B ∪ S| = |B| + |S| − |B ∩ S|.
There are 27 students and 4 play neither, so |B ∪ S| = 27 − 4 = 23. Thus
23 = 11 + 18 − |B ∩ S| ⇒ |B ∩ S| = 29 − 23 = 6.
Probability a randomly chosen student plays both = 6/27 = 2/9.
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