There are 100 freshman students at a school. The probability that a freshman plays a sport is 0.55. The probability that a fresh

The likelihood that a freshman at this institution participates in either sports or music is 0.74

Step-by-step explanation:

The principles of probability addition are:

• P(A or B) = P(A) + P(B) when events are mutually exclusive (cannot occur simultaneously)
• P(A or B) = P(A) + P(B) - P(A and B) when they are non-mutually exclusive (if there’s a shared outcome)

Since the chance of a freshman engaging in sports is 0.55

∴ P(sport) = 0.55

The chance of a freshman playing a musical instrument is 0.34

∴ P(music) = 0.34

The probability that a freshman is involved in both activities is 0.15

∴ P(sport and music) = 0.15

To determine the probability of a freshman engaging in sports or music, we use the second principle as 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 chance that a freshman at this school participates in either sports or music is 0.74

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