By definition of probability, the correct answer is option D.: the probability that a student plays either football or baseball is 30%.
What is Probabitity
Probability is the greater or lesser possibility that a certain event will occur.
In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
What is Union of events
The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
Probability that a student plays either football or baseball
In first place, let's define the following events:
- F: The event that represents the amount of students that play football.
- B: The event that represents the amount of students that play baseball.
Then you know:
- P(F)= 22%= 0.22
- P(B)= 12%= 0.12
- Eight students play on both teams → P(F and B)= P(F∩B)= [tex]\frac{8}{200}[/tex]×100= 4%= 0.04 [The intersection of events, A ∩ B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A ∩ B is verified when A and B occur simultaneously.]
In this case, considering the definition of union of events, the probability that a student plays either football or baseball is calculated as:
P(F∪B)= P(F) + P(B) -P(F∩B)
P(F∪B)= 0.22 + 0.12 -0.04
P(F∪B)= 0.30 = 30%
Then, the correct answer is option D.: the probability that a student plays either football or baseball is 30%.
Learn more about probability:
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