Survey: Customer Loyalty Are customers more loyal in the east or in the west? The following table is based on information from Trends in the United States, published by the Food Marketing Institute, Washington, D.C. 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	54	59	112	77	118	452
Midwest	31	68	68	120	63	173	523
South	53	92	93	158	106	158	660
West	41	56	67	78	45	86	373
Column Total	157	270	287	468	291	535	2008

What is the probability that a customer chosen at random

(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.