# 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 is**both a student and favors having an ethics course as a graduation requirement is 0.3. **

- 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 **

- 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)

- 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. **