Expected Value

Finite Math

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KM1.

The expected value of a benefit is given by the weighted average of the benefits formula below.

In which case is the probability of an even occurring and is the event itself. This can be tabulated as below.

1 0.6 20 12

2 0.4

In this case the decision criteria should be based on the situation which with regards to the expected costs. Any condition that at least produces the expected value is good. This would include the interventions that that produce outcomes that are equal to or greater than the expected value (Shifts, 2009).

Since success of the medical treatment promises 20 more years of expectancy which is greater than the expected value, I would pursue it. The failure guarantees a survival of for less than 5 years which is far below the expected value which is greater than 12 but less than 14. Based on the expected value of this situation I would seek treatment to increase my life expectancy.

I would agree with this decision because I prefer a higher life expectancy.

KM2.

The success of the medical treatment promises 20 more years of expectancy which is greater than the expected value, I would pursue it. The failure guarantees a survival of for less than 5 years which is far below the expected value which is greater than 12 but less than 14. It is clear that the 20 additional years are still valid at 60% probability three years after. In the scenario that our health does not deteriorate and we remain stable in terms of health, the treatment will still be expected to add 20 years with the same chance of success. At that point the choice is no brainier given that we have at most 2 years to live without it. On the other hand, positive outcome is given as 0.6*20 years = 12 years while the negative outcome given as 0.4*2 years = 0.8 years. In this scenario we can find the net outcome as the difference between the two extremes that is 11.2 years (Shifts, 2009).

SM3.

In statistics and probability theory, the median refers to the numerical value that separates the higher half of the data sample or the population or the probability distribution from the other (lower) half. For a finite list of numbers the median