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
For further information:
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