Chapter 04, Supplementary Exercises, Problem 097a A random sample of 400 college

Question

Chapter 04, Supplementary Exercises, Problem 097a A random sample of 400 college students was asked if college athletes should be paid. The following table gives a two-way classification of the responses. nould Not Be Paid 10 ! 90 210 Student athlete Student nonathlete 90 Round your answers to three decimal places. 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. ii is an athlete and favors paying stude iv. is a nonathlete or is against paying student athletes.

Explanation / Answer

i) P(in favor of playing college athletes) = 300/400 = 0.75

ii) P(favor of playing college athletes | the student selected not athlete) = P (favor of playing college athletes and the student selected not athlete) / P(the student selected not athlete) = (210/400) / (300/400) = 0.7

iii) P (is an athlete and favor paying student athlete) = 90/400 = 0.225

iv) P(non athlete or is against paying student athlete) = P(non athlete) +P(against paying student athlete) - P(non athlete and against paying student athlete) = 300/400 + 10/400 - 100/400 = 180/400 = 0.525

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