REVISING PROBABILITIES ACCORDING T O NEW INFORMATION: A FUNDAMENTAL STOCHASTIC INTUITiON

Manfred Borovcmik
unpublished
Probability judgements may have t o be revised if new information is available. From the mathematical perspective probability revisions are intimately connected t o the notion of conditional probability and Bayes' formula, a subsidiary concept and a t r i v i a l theorem respectively. Nevertheless empirical investigations i n subjects' understanding of probability do indicate t h a t people do not cope adequately w i t h situations involving probability revisions, if they have been taught t h e
more » ... mathematical concepts o r not does not matter. I n what follows I will try t o sketch some phenomena of misunderstanding, give some comments on the interplay between mathematics and intuitions which I t h i n k represents the origin of lack o f comprehension. A b r i e f overview on the favor concept should enable the impression t h a t by way of teaching t h i s concept probabilistic reasoning could be improved. 4. Examples-Phenomena Example 1 : "Falk Phenomenon" Two marbles are drawn without replacement from t h e u r n above. The question f o r t h e probability t o get a white marble a t second t r y if one has drawn a white one a t f i r s t try, let us denote t h a t by P(W1 I I w,) , does not cause any particular problem and i s usually answered with 1/3. However , many subjects fail t o solve t h e "reverse" problem, namely t o evaluate P(W1 IWII) (see Falk, 1983). They will argue: The colour of the second marble cannot influence t h a t of t h e marble drawn a t f i r s t. This missing causal influence induces them t o t h i n k as if WI be stochas-tically independent of WI 1. There is an intermixture of probabilistic reasoning and causal inference. T w o o f many possible reasons f o r t h a t are: a) Conditional probabilities are usually applied i n "forward looking" situations , a t least u n t i l Bayes' formula is dealt with. An u r n represents the situation and the probability t o calculate: ICOTS 2, 1986: Manfred G. Borovcnik
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