C. The probability that the student takes Spanish or French is 23%
What is mutually exclusive events ?
If two events can not occur together at same time, then the events are called mutually exclusive.
If two events are mutually exclusive, then,
P(A∪B) = P(A)+P(B)
And If two events are not mutually exclusive, then,
P(A∪B) = P(A)+P(B)-P(A∩B)
What is the required probability ?
In central high school,
15% of the students take Spanish language = P(A) (say)
12% of the students take French language = P(B) (say)
& 4% of the students take both the languages = P(A∩B)
Since some of students take both languages, so this is not mutually exclusive.
The probability that the student takes Spanish or French is P(A∪B).
∴ P(A∪B) = P(A)+P(B)-P(A∩B)
= 15%+12%-4%
= [tex]\frac{15}{100}+\frac{12}{100}-\frac{4}{100}[/tex]
= [tex]\frac{15+12-4}{100}[/tex]
= [tex]\frac{23}{100}[/tex] = 23%
Hence, Required probability is 23%
Learn more about mutually exclusive events here :
https://brainly.com/question/3550010
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