I'm working on a formula for measuring decision making skill and am
trying to estimate the probability that a person of known skill can
distinguish among different response option contrasts and avoid a type
II error. The problem actually breaks down to a rather simple analogy:
Imagine that a man has been sentenced by court to run a gauntlet
composed of four club-wielding executioners. The court places the best
execution at the beginning of the gauntlet followed by the second,
third and fourth best. Based on past performance the first executioner
has a .90 probability of striking the man, while the remaining
executioners have .50, .30, and .20 respectively. What is the man's
probability of being struck by at least one of the executioners and
how is this calculated?
Notice that the events are not independent because if the man is fast
enough to make it past the first executioner his odds of making it
past the rest are improved since he will have survived the best
executioner.
What is this sort of problem called? (e.g., conditional probability,
joint probability, Baysian probability, etc.). Please excuse the
inanity of the example but it is much easier than trying to explain my
research.
Peter
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