Calculating Probabilities from a Table: Ethics Course Requirement

Classified in Mathematics

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Faculty and Student Responses

A university president proposed that all students must take a course in ethics as a requirement for graduation. The table below gives the responses of a sample of faculty and students at the university when asked their opinion on this issue.

Y: FAVOR O: Oppose N: Neutral

Totals

F: Faculty         45             15             10                    70

S: Student        90             110             30                  230

Totals   135               125                40

Probabilities

1. Find the following probabilities; each time ONE person is being randomly selected.

P(S or Y) = (230 + 135 – 90)/300 = 275/300 = 0.917

Description: The probability that the randomly selected person is  a student or favors having an ethics course as a  graduation requirement or both is 0.917.

P(S and Y) = 90/300 = 0.3

Description: The probability that the randomly selected person isboth a student and favors having an ethics course  as a graduation requirement is 0.3.

1. P(S|Y) = 90/135 = 0.667

Description: The probability that the randomly selected person is a student knowing that the selected person favors having  an ethics course as a graduation requirement is 0.667

1. What is the probability of randomly selecting three different people that are neutral about this ethics course proposal?  Show work, listing the probabilities used in the calculation.

40   x   39   x   38  =  0.002

300     299      298

(NOTE – on calculator:  40*39*38/300/299/298 = .0022176831)

1. Identify a PAIR of mutual exclusive events for this problem about the responses of a sample        of faculty and students at the university when asked their opinion on an ethics course being  required for graduation and explain why they are mutually exclusive.

Answers will vary; row events are mutually exclusive of each other and column events are mutually exclusive of each other.

Sample answer:   “Selecting a person who opposes having an ethics course as graduation requirement” and “selecting a person who is neutral about having an ethics course as a graduation requirement” are mutually exclusive because one person cannot be both opposing and neutral about the issue.