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.

	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).

Answer 1