A Local Business a Has Two Competitors, B and C

Multiple Choice

A local business A has two competitors, B and C. No customer patronizes more than one of these businesses at the same time. Initially, the probabilities that a customer patronizes A, B, or C are 0.4, 0.4, and 0.2, respectively. Suppose A initiates an advertising campaign to improve its business and finds the following transition matrix to describe the effect. ​ ​
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If A runs the advertising campaign for 3 weeks, find the probability that a customer will still patronize business B.
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A) 0.0640
B) 0.2960
C) 0.1280
D) 0.0960
E) 0.2888