Double counting (fallacy)
Encyclopedia
Double counting is a fallacy in which, when counting events or occurrences in probability
or in other areas, a solution counts events two or more times, resulting in an erroneous number of events or occurrences which is higher than the true result. This results in the calculated sum of probabilities for all possible outcomes to be higher than 100%, which is impossible.
For example, what is the probability of seeing at least one 5 when throwing a pair of dice? An erroneous argument goes as follows: The first die shows a 5 with probability 1/6; the second die shows a 5 with probability 1/6; therefore the probability of seeing a 5 is 1/6 + 1/6 = 1/3 = 12/36. However, the correct answer is 11/36, because the erroneous argument has double-counted the event where both dice show 5s. The inclusion-exclusion principle can be used to compensate for double counting by subtracting those objects which were double counted.
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
or in other areas, a solution counts events two or more times, resulting in an erroneous number of events or occurrences which is higher than the true result. This results in the calculated sum of probabilities for all possible outcomes to be higher than 100%, which is impossible.
For example, what is the probability of seeing at least one 5 when throwing a pair of dice? An erroneous argument goes as follows: The first die shows a 5 with probability 1/6; the second die shows a 5 with probability 1/6; therefore the probability of seeing a 5 is 1/6 + 1/6 = 1/3 = 12/36. However, the correct answer is 11/36, because the erroneous argument has double-counted the event where both dice show 5s. The inclusion-exclusion principle can be used to compensate for double counting by subtracting those objects which were double counted.