Question

SG#14

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	36	59	112	77	108	424
Midwest	31	47	68	120	63	178	507
South	53	107	93	158	106	205	722
West	41	32	67	78	45	71	334
Column Total	157	222	287	468	291	562	1987

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.

No. P(loyal 15 or more years) ? P(loyal 15 or more years | East).Yes. These events can occur together.    Yes. P(loyal 15 or more years) = P(loyal 15 or more years | East).No. These events cannot occur together.

Answer 1

Probabaility = number of favourable event / total number of event
a) has been loyal 10 to 14 years
= 291/1987

here total = 1987 and number of people who are loyal in 1014 years = 291
hence 291/1987

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

P(A |B) = P(A and B)/P(B)
= 77/424

(c) has been loyal at least 10 years
=(291 + 562)/1987
= 853/1987

(d) has been loyal at least 10 years, given that he or she is from the West
=(45+71)/334
=126/334

(e) is from the West, given that he or she has been loyal less than 1 year
=41/157

(f) is from the South, given that he or she has been loyal less than 1 year

=53/157

Please rate.