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# Probability of Higher Education Institutions

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Public Private Total
Northeast 6 14 20
Mideast 4 12 16
South 15 9 24
West 15 25 40
Total 40 60 100

The following contingency table above cross classifies institution of higher education in the United States by region and type.

Suppose an institution of higher education is selected at random. Determine the probability that the institution obtained:

is in the West
is in the Mideast and Public
is a private institution or in the West
is a Public institution GIVEN the institution is in the northeast
is in the Mideast and Northeast

The following question about the variable in the contingency table

Name the two variable that are mutually exclusive?
Name the two variables that are compliments of each other?

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#### Solution Preview

Total no. of institutes:
n = 20+16+24+40 = 100
Number of institutes in West, nWest = 40
Hence, probability of the institute in the West = nWest/n = 40/100 = 0.4

n(Mideast & Public) = 4
Hence, probability of Mideast and Public = 4/100 = ...

#### Solution Summary

A problem of probability estimation for different conditions of a contingency table is solved here.

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