Use the following information to answer question. A company is considering what size copying machine it should lease. The copier comes in three different sizes: small, medium, and large. A larger machine can handle more work, but it also costs more. The demand for the machine in the next year is uncertain. The cost of leasing a smaller machine is lower than the cost of leasing a larger one. However, at those times when the small machine could not handle the high demand, the company would have to lease a second machine and pay a significantly higher cost than if it had leased a larger machine in the first place.
The possible costs of leasing the three different copiers under conditions of low and high demand are presented in the following table.

An economic consultant predicts that the demand for the machine will be high the next year and suggests that the company should therefore lease a large machine.

Assume that the consultant has the following track record of predicting demand.

where I₁ indicates that the consultant predicts S₁ and I₂ indicates that the consultant predicts S₂. Do you agree with the consultant’s advice?

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Size of copier Small Medium Large Pr(S) Future demand Low (S) 400 500 600 .4 High(S) 800 900 600 .6