New parents in a little town buy two major brands of infant formulas, labeled A and B. After some intensive study, a marketing researcher for one of the manufacturers found that the probability of parents purchasing A or B is based on the parents’ most recent purchase. Suppose that the following transition probabilities are appropriate 1. Given a parent initially purchased Brand B, the probability that this parent purchases Brand A on the second purchase is
A) (0.75)(0.75)+(0.25)(0.20) = 0.5625 + 0.0500 = 0.6125
B) (0.20)(0.25)+(0.80)(0.80) = 0.0500 + 0.6400 = 0.6900
C) (0.20)(0.75)+(0.80)(0.20) = 0.1500 + 0.1600 = 0.3100
D) (0.75)(0.25)+(0.25)(0.80) = 0.1875 + 0.2000 = 0.3875
E) None of the above
2. Given a parent initially purchased Brand B, the probability that this parent purchases Brand B on the second purchase is
A) (0.75)(0.75)+(0.25)(0.20) = 0.5625 + 0.0500 = 0.6125
B) (0.20)(0.25)+(0.80)(0.80) = 0.0500 + 0.6400 = 0.6900
C) (0.20)(0.75)+(0.80)(0.20) = 0.1500 + 0.1600 = 0.3100
D) (0.75)(0.25)+(0.25)(0.80) = 0.1875 + 0.2000 = 0.3875
E) None of the above