From two grocery stores, a survey is provided for the preference of breads marked as A, B and C.
a) Draw a tree diagram depicting the sample space outcomes for the test results.
b) List the sample space outcomes that correspond to each of the following events:
b.1 Both stores prefer bread A.
b.2 The two stores prefer the same bread.
b.3 The two stores prefer different breads.
b.4 Bread A is preferred by at least one of the two stores.
b.5 Neither of the stores prefers bread C.
c) Assume all sample space outcomes are equally likely, find the probability of each of the events of part b.
Suppose that Bread A’s baker claims that 80 percent of all people prefer bread A and that only 10 percent prefer each of breads B and C. Answer the following questions.
d) Assuming that the baker’s claim is true and that the two taste test participants make independent bread preference decisions. Determine the probability of each sample space outcome. e) Find the probability that neither taste test participant will prefer bread A.
f ) If, when the taste test is carried out, neither participant prefers bread A, use the probability you computed in part e to decide whether the distributor’s claim seems valid. Explain.
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