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9. Three antibiotics A1, A2, and A3 and five types of bacilli B1, B2, B3, B4, and By are involved in a study of the effectiveness of antibiotics and bacilli, with Aj having a probability of 0.3 of destroying B1, and so on. Without knowing the proportion in which these germs are distributed in an epidemic, in what ratio should the antibiotics be mixed to have the greatest probability of being effective? B1 B2 B3 BA B5 A1 0.3 0.4 0.5 1 10 A2 |0.2 0.3 0.6 0 1 A3 0.1 0.5 0.3 0.1 0 10. In a certain community there are three grocery stores A, B, and C. Each month, store A retains 90% of its customers and loses 10% of them to store B. Store B retains 5% of its customers and loses 85% to store A and 10% to store C. Store C retains 40% of its customers and loses 50% of them to store A and 10% to store B. The transition matrix P is A B C P = A 0.90 0.10 0 B 0.85 0.05 0.10 0.50 0.10 10.40 Suppose on January 1, 7 shopped at store A, ; shopped at store B, and 1 shopped at store C. (a) What proportion of customers will each store retain by March 1? (b) In the long run what will be the distribution of customers between the stores? 2 6/11 e x 1 WE