Are customers more loyal in the East or in the West? The following table is base

Question

Are customers more loyal in the East or in the West? The following table is based on information from a recent study. The columns represent length of customer loyalty (in years) at a primary supermarket. The rows represent regions of the United States. What is the probability that a customer chosen at random has the following characteristics? (Enter your answers as fractions.) (a) has been loyal 10 to 14 years 97/691 (b) has been loyal 10 to 14 years, given that he or she is from the East 77/482 (c) has been loyal at least 10 years 284/691 (d) has been loyal at least 10 years, given that he or she is from the West 41/120 (e) is from the West, given that he or she has been loyal less than 1 year (f) is from the South, given that he or she has been loyal less than 1 year (g) has been loyal 1 or more years, given that he or she is from the East (h) has been loyal 1 or more years, given that he or she is from the West

Explanation / Answer

e) This is a case of conditional probability:

Probability = 41/157

f) This is a case of conditional probability:

Probability = 53/157

g) This is a case of conditional probability:

Probability = (482 - 32)/482 = 450/482

h) This is a case of conditional probability:

Probability = (360 - 41)/360 = 319/360

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