Mathematical

Question 1

PROBABILITY // Gambler’s Fallacy

Answer 1

Monte Carlo Fallacy
Fallacy of the Maturity of Chances

the false belief than a statistically independent probability is affected by past results

“I’ve flipped 9 heads in a row - the next flip MUST be a tails!”

Question 2

PROBABILITY // Inverse Gambler’s Fallacy

Answer 2

the false belief that observing an unlikely result to a random process implies numerous prior iterations of the process

“that guy just rolled double-six; he must have been rolling for some time to get that!”

Question 3

PROBABILITY // Prosecutor’s Fallacy

Answer 3

cf. Defence Attorney’s Fallacy

a misunderstanding of conditional probability, in believing that a low probability of matches implies a low probability of ANY matches being found

“The odds of winning the lottery are too low to believe anyone actually wins it!”

Question 4

PROBABILITY // Retrospective Determinism

Answer 4

the fallacious belief that any true event was inevitable; that given that it happened, the probability of it happening (prior to the fact) was 100%

P occured
therefore, P was always going to occur

“John’s marriage has made him miserable, so it must have been inevitable he’d be an unhappy husband”

Question 5

STATISTICS - Double Counting

Answer 5

counting the same event in a statistical argument multiple times, leading to a false conclusion

“I need ten pallets: one for each colour of the rainbow, and three for the primary colours”

Question 6

STATISTICS - Ecological Fallacy

Answer 6

Ecological Inference Fallacy
Population Fallacy

inferring the nature of an individual from inferences on the group the individual belongs to; affected by mean and group averages

“there are 100 black men in the town, and 10% of the town are in the KKK, therefore the number of black men in the KKK here is 10% of 100 = 10”

“immigrants are more likely to be illiterate, yet states with more immigrants have lower levels of illiteracy”

Question 7

STATISTICS - Ludic Fallacy

Answer 7

the faulty application of limited statistical models to inapplicable real-life scenarios

“A: This coin has flipped 1000 heads in a row, but I know the odds of it coming up tails are 1/2.
B: This is the real world, not a model. At some point you have to consider that the coin is dishonest.”

Question 8

STATISTICS - Quantitative Fallacy

Answer 8

McNamara Fallacy

only considering quantitative, measurable factors at the ignorance of the qualitative

“A: We win wars by killing soldiers, so let’s track how many insurgents we’ve killed.
B: The more insurgents we kill, the more we inspire to join!”