There are 24 students in the class. If 12 of them enrolled to the French courses, 13 of them to the Spanish and 7 of them take neither, what is the probability that a randomly-chosen student from this group is taking only the French class?

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Mathematics

31 August, 20:32

There are 24 students in the class. If 12 of them enrolled to the French courses, 13 of them to the Spanish and 7 of them take neither, what is the probability that a randomly-chosen student from this group is taking only the French class?

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Answers (1)

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Kamden · Answer 1

1/6 = 0.1667 = 16.67%

Step-by-step explanation:

If there are 24 students in the class and 7 of them take neither courses, we have 17 students that take one or both courses.

To find the students that took both courses, we can use the formula:

N (Spanish or French) = N (Spanish) + N (French) - N (Spanish and French)

17 = 13 + 12 - N (Spanish and French)

N (Spanish and French) = 8

Then, the number of students that are taking only French is:

N (only French) = N (French) - N (Spanish and French)

N (only French) = 12 - 8 = 4

So the probability of chosing a student that took only French is:

P (only French) = N (only French) / N (total)

P (only French) = 4 / 24 = 1/6