Question

A school has 100 students. Among them, 60 students play foorball, 50 students play basketball, and...

A school has 100 students. Among them, 60 students play foorball, 50 students play basketball, and 30 students play both football and basketball.

A) Use Inclusion/Exclusion rule to find out how many students play either football or basketball (or both).
B) if two students are randomly selected from this school, what is the probability of the evenet in which both of them play neither football nor basketball?

Math   Statistics-And-Probability   
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Answer #1

A school has 100 students. Among them, 60 students play football, 50 students play basketball, and 30 students play both football and basketball.

  1. Use Inclusion/Exclusion rule to find out how many students play either football or basketball (or both).

Playing football or basketball = playing football + playing basketball- (both football and basketball).

Playing football or basketball = 60+50-30

=80

B) if two students are randomly selected from this school, what is the probability of the event in which both of them play neither football nor basketball?

Playing football or basketball =80

Playing neither football nor basketball = 100-80=20

P(one student Playing neither football nor basketball) = 20/100 = 0.2

P(Two students Playing neither football nor basketball) = 0.2*0.2

=0.04

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