There are two alternative routes joining two villages, and the cost of maintaining each route is c per year. The probablility of blockage for a maintained route is p and for an unmaintained route is 1. The cost of of there being no unblocked route between the village is b. calculate the expected costs of the following strategies: S0 - maintain neither route; S1 - maintain just one route; S2 - maintain both routes.

The answer for S0 is b, S1 is c+pb, S2 is 2c+b*p^2

but i don't know how to get these answers, can anyone please help me and show me the steps please?

thanks a lot!!

S0 - both routs will be blocked with prpbability 1, so expected cost is b

S1 - fixed cost is c the cost of maintaining one of the routs, and a cost of b which is incured if the maintained rout becomes blocked with probability p. So expected cost is c+pb

S2 - fixed cost 2c to maintain both routs, and an additional cost of b which is incred if both route become blocked which happens with probability p^2. So expected cost is 2c+p^2 b

RonL

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