Also, what exactly what do they mean when they say “outcomes”? Different services and projects have different outcomes, some of which are more closely tied to service units than others. Also, sometimes the definitions and / or reporting requirements are sometimes so complex that they are not only onerous, but obscure more than they illuminate. For example, I recently heard a news report on the issue of outcomes reporting where someone said in all seriousness that outcomes reporting is hard because you need people with appropriate degrees to manage this.
The simple solutions above show that a player with a strategy of switching wins the car with overall probability 2 / 3 , ., without taking account of which door was opened by the host ( Grinstead and Snell 2006:137–138 Carlton 2005 ). In contrast most sources in the field of probability calculate the conditional probabilities that the car is behind door 1 and door 2 are 1 / 3 and 2 / 3 given the contestant initially picks door 1 and the host opens door 3 ( Selvin (1975b) , Morgan et al. 1991 , Chun 1991 , Gillman 1992 , Carlton 2005 , Grinstead and Snell 2006:137–138 , Lucas et al. 2009 ). The solutions in this section consider just those cases in which the player picked door 1 and the host opened door 3.
First, it is not always true in practice. A theoretical polynomial algorithm may have extremely large constant factors or exponents thus rendering it impractical. On the other hand, even if a problem is shown to be NP -complete, and even if P ≠ NP , there may still be effective approaches to tackling the problem in practice. There are algorithms for many NP -complete problems, such as the knapsack problem , the traveling salesman problem and the Boolean satisfiability problem , that can solve to optimality many real-world instances in reasonable time. The empirical average-case complexity (time vs. problem size) of such algorithms can be surprisingly low. An example is the simplex algorithm in linear programming , which works surprisingly well in practice; despite having exponential worst-case time complexity it runs on par with the best known polynomial-time algorithms.