Question

Th llowng table is based on information from Trends in the United Suates. A survey of 2008 customers was taken and the length of customer loyalty (in years) nt a primary supermarket is broken corresponding event is designated in parentheses. by Loyalty (years) Midwest (F) South (G) West (H) 32 31 53 41 113 136 18S 123 189 183 264 123 118 173 158 86 Draw a Venn diagram to illustrate this sample space. Attach the Venn diagram to the homework. a. (6 points) Suppose a customer is chosen at random from this survey est? b. What is the probability that the customer has been loyal 1-4 years and is from the Midw 3) What is the probability that the customer is from the East or has been loyal 5-14 years? c. 3) d. If the customer was from the South, what is the probability that he or she was loyal for 15 or more years? e. If the customer was loyal for 15 or more years, what is the probability that he or she is from the South? ts D and G are mutually exclusive? Use the mathematical definition of mutually exclusive (3 points) events as support for your decision. Are the events D and G independent? for your decision. Use the mathematical definition of independent events as support g. (3 points)

Answer 1

b) P(F and B) = 136/2008 = 0.0677

c) P(E or C) = P(E) + P(C) - P(E and C) = (452 + 759 - 189)/2008 = 0.5090

d) P(D | G) = P(D and G)/P(G) = 158/660 = 0.2394

e) P(G | D) = P(G and D)/P(D) = 158/535 = 0.2953

f) P(D and G) = 158/2008 = 0.0787

Since P(D and G) $\neq$ 0, so the events D and G are not mutually exclusive.

g) P(D and G) = 158/2008 = 0.0787

   P(D) * P(G) = 535/2008 * 660/2008 = 0.0876

Since P(D and G) $\neq$ P(D) * P(G), so the events D and G are not independent.