Question

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

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.

Less Than 1 Year 1-2 Years 3-4 Years 5-9 Years 10-14 Years 15 or More Years Row Total
East 32 59 59 112 77 102 441
Midwest 31 40 68 120 63 190 512
South 53 74 93 158 106 174 658
West 41 68 67 78 45 61 360
Column Total 157 241 287 468 291 527 1971

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


(b) has been loyal 10 to 14 years, given that he or she is from the East


(c) has been loyal at least 10 years


(d) has been loyal at least 10 years, given that he or she is from the West


(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


(i) Are the events "from the East" and "loyal 15 or more years" independent? Explain.

Yes. P(loyal 15 or more years) = P(loyal 15 or more years | East).

Yes. These events can occur together.     

No. These events cannot occur together.

No. P(loyal 15 or more years) ≠ P(loyal 15 or more years | East).

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