1.Each of the two supermarket chains proposes to build a store in a rural region that is served by three towns. The distances between towns A, B and C are shown in Figure below.

10 miles15 miles

20 miles

Approximately 45% of the region's population live near town A, 35% live near town B and 20% live near town C.If both chains locate in the same town or equidistant from a town, chain I will control 65% of the business in that town. If chain I is closer to a town than chain II, chain I will control 90% of that town's business. If chain I is farther from a town than chain II, it will still draw 40% of that town's business. The remaining business under all circumstances will go to chain II.

What is the probability that a randomly chosen resident from this rural region shops in chain I,

a.If chain I locates in town A and chain II locates in town C?

b.If chain I locates in town B and chain II locates in town C?