A : A complete suspension of diplomatic relations between the USA and Russia, sometime in 2023.
B : A Russian invasion of Poland, sometime in 2023.
C : Chicago Bulls winning NBA competition, sometime in 2023.
D ⇔ A & B
E ⇔ A & C.
In order to estimate the likelyhood of an event, the mind looks in the available memory for information. The more easily available an information the more it is taken into account.
A and B hold information that is relevent to each other. A and B are correlated and the occurence of one of them strengthens the probability of the other happening. The mind while trying to evaluate the likelyhood of each of the components of D takes one as a relevant information about the other hence leading to overestimate p(A) and p(B).
p(D) = p(A&B) = p(A).p(B | A) = p(B).p(A | B)
Then the mind gets it wrong is when it makes the above equation equal to either p(A | B) or p(B | A) or oddly equal to their sum, as it has been mentionned in previous comments.
The intuitive mind has trouble understanding probability multiplication. It rather functions in an addition (for correlated events) and substraction (for independent events) mode when evaluating likelyhood. p(E) for example is likely to be seen as p(C) - p(A). C is a more likely event ( even more if you live in Chicago) than A. Let say 5% for C and to be generous 1% for A.
The mind would rather do p(E) = p(C) - p(A) = 4 % which ends up making p(A&C) > p(A) ,
rather than the correct p(A) . p(C |A) = p(C) . p(A | C) = p(A) . p(C) = 0.05 % assuming A and C completely independent.
The great speed at which the intuitive mind makes decisions and assigns likelyhood for propositions seems to be at the expense of occuracy due to oversimplification, poor calculus ability, sensitivity to current emotional state leading to volatility of priority order, sensitivity to chronology of information acquisition… etc.
Nevertheless, the intuitive mind shared with other species proved to be a formidable machine fine tuned for survival by ages of natural selection. It is capable of dealing with huge amount of sensorial and abstract information gathered upon time, sorting it dynamically, and making survival decisions in a second or two.
A : A complete suspension of diplomatic relations between the USA and Russia, sometime in 2023.
B : A Russian invasion of Poland, sometime in 2023.
C : Chicago Bulls winning NBA competition, sometime in 2023.
D ⇔ A & B
E ⇔ A & C.
In order to estimate the likelyhood of an event, the mind looks in the available memory for information. The more easily available an information the more it is taken into account.
A and B hold information that is relevent to each other. A and B are correlated and the occurence of one of them strengthens the probability of the other happening. The mind while trying to evaluate the likelyhood of each of the components of D takes one as a relevant information about the other hence leading to overestimate p(A) and p(B).
p(D) = p(A&B) = p(A).p(B | A) = p(B).p(A | B)
Then the mind gets it wrong is when it makes the above equation equal to either p(A | B) or p(B | A) or oddly equal to their sum, as it has been mentionned in previous comments.
The intuitive mind has trouble understanding probability multiplication. It rather functions in an addition (for correlated events) and substraction (for independent events) mode when evaluating likelyhood. p(E) for example is likely to be seen as p(C) - p(A). C is a more likely event ( even more if you live in Chicago) than A. Let say 5% for C and to be generous 1% for A.
The mind would rather do p(E) = p(C) - p(A) = 4 % which ends up making p(A&C) > p(A) ,
rather than the correct p(A) . p(C |A) = p(C) . p(A | C) = p(A) . p(C) = 0.05 % assuming A and C completely independent.
The great speed at which the intuitive mind makes decisions and assigns likelyhood for propositions seems to be at the expense of occuracy due to oversimplification, poor calculus ability, sensitivity to current emotional state leading to volatility of priority order, sensitivity to chronology of information acquisition… etc.
Nevertheless, the intuitive mind shared with other species proved to be a formidable machine fine tuned for survival by ages of natural selection. It is capable of dealing with huge amount of sensorial and abstract information gathered upon time, sorting it dynamically, and making survival decisions in a second or two.