There are 100 freshman students at a school. The probability that a freshman plays a sport is 0.55. The probability that a freshman plays a musical instrument is 0.34. The probability that a freshman plays both a sport and a musical instrument is 0.15. What is the probability that a freshman student at this school plays either a sport or a musical instrument?

P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen at the same time)
P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they have at least one outcome in common)

∵ The probability that a freshman plays a sport is 0.55

∴ P(sport) = 0.55

∵ The probability that a freshman plays a musical instrument is 0.34

∴ P(music) = 0.34

∵ The probability that a freshman plays both a sport and a musical

instrument is 0.15

∴ P(sport and music) = 0.15

To find the probability that freshman student at this school plays either a sport or a musical instrument use the second rule above because it is non-mutually exclusive

∵ P(sport or music) = P(sport) + P(music) - P(sport and music)

∴ P(sport or music) = 0.55 + 0.34 - 0.15

∴ P(sport or music) = 0.74

The probability that a freshman student at this school plays either a sport or a musical instrument is 0.74

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