TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/1.4

A random sample of 400 college students was asked if college athletes should be payed. The following table gives a two-way classification of the responses.

	Should be paid	Should not be paid
Student athlete	90	10
Student nonathlete	210	90

(a) If one student is randomly selected from these 400 students, find the probability that this student

i. is in favor of paying college athletes

ii. favors paying college athletes given that the student selected is a nonathlete

iii. is an athlete and favors paying student athletes

iv. is a nonathlete or is against paying students athletes

(b) Are the events student athlete and should be paid independent? Are they mutually exclusive? Justify your answer.

Lösungsvorschlag von Gittenburg

--Gittenburg 08:26, 13. Okt. 2019 (CEST) a)

i) $(90+210)/400=0.75$

ii) $210/300=0.7$

iii) ${\frac {100}{400}}\cdot {\frac {90}{100}}={\frac {9}{40}}=0.225$

iv) $300/400+10/400=0.775$

b)

• not independent because P("student athlete" and "should be paid") is not equal to P("student athlete") * P("should be paid")
• not mutually exclusive because there are 90 student athletes in favor of getting paid.