\"Harry-Potter\" For the Triwizard Tournament 60 of 280 students have reached th

Question

"Harry-Potter"
For the Triwizard Tournament 60 of 280 students have reached the minimum age of 17 to apply to the tournament.
10 of the students above full age (18 y/o or older) have applied with a note with their names in the goblet of fire. But also 15 of the underaged students are trying to outwit the age limit of the goblet of fire.

1) You observe a student trying to put a note with his name in the goblet of fire. What is the probability that this student is underaged?

2) You met a student, who did not put a note with his name in the goblet of fire. What is the probability that this student is of full age?

Explanation / Answer

60 students are eligible

1)
15 students are trying to outwit the age limit.
Hence probability that a student is underaged = 15/260 = 0.0577

2)
P(E|A') = P(E and A')/P(A')

E - Eligible student
A' - students who did not apply
P(A') = (280-25)/280 = 0.9107

P(E and A') = 60/280 = 0.2143

P(E|A') = 0.2353 (Required probability)

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