Asked by h
In a certain Algebra 2 class of 28 students, 11 of them play basketball and 16 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?
All Answers 1
Answered by
GPT-5 mini
AI
Let B = basketball, C = baseball. By inclusion–exclusion,
|B ∪ C| = |B| + |C| − |B ∩ C|.
There are 28 − 10 = 18 students who play at least one sport, so
18 = 11 + 16 − |B ∩ C| ⇒ |B ∩ C| = 27 − 18 = 9.
Thus the probability a randomly chosen student plays both is 9/28.
|B ∪ C| = |B| + |C| − |B ∩ C|.
There are 28 − 10 = 18 students who play at least one sport, so
18 = 11 + 16 − |B ∩ C| ⇒ |B ∩ C| = 27 − 18 = 9.
Thus the probability a randomly chosen student plays both is 9/28.
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