TABLE 1.

Experimental design—Bayesian probability of box A (Bpr) given base rates and evidence (#stimuli per odds‐evidence combination shown in parenthesis)

Evidence in favor of LEFT Box (has 2 black balls 1 white ball)
Prior Odds of LEFT Box Selection	Black Balls = 0	Black Balls = 1	Black Balls = 2	Black Balls = 3	Black Balls = 4	Black Balls = 5	Total n
0/6						Bpr = 0.00	1
1/6				Bpr = .29	Bpr = .62	Bpr = .86	3
2/6			Bpr = .20	Bpr = .50	Bpr = .80	Bpr = .94	4
3/6		Bpr = .11	Bpr = .33	Bpr = .67	Bpr = .89		4
4/6	Bpr = .06	Bpr = .20	Bpr = .50	Bpr = .80			4
5/6	Bpr = .13	Bpr = .38	Bpr = .71				3
6/6	Bpr = 1.00						1
Total n	3	3	4	4	3	3	TOTAL STIMULI = 20

Note: Of the total possible combinations of prior odds and evidence, the indicates cells show the stimuli used and the Bayesian probability (Bpr) of that particular “Evidence” and “Prior Odds” combination for the stimulus. We classified 14 Hard (shaded) and six Easy (dashed border) trials among the set of 20 stimuli presented to each participant. Two degenerate choices (the extreme probabilities of 1 and 0) should constitute an “easy” choice for one fully understanding the task, but we employed the convention to label as “Hard Trials” those trials where the evidence and the prior odds point to opposing boxes (eg, Evidence indicated a more likely LEFT box used, but the Prior Odds indicated a more likely RIGHT box used). This is a more defensible categorization of Hard vs Easy trials given our modification of the task to elicit probabilities rather than a dichotomous response of Left or Right (in which case Bayesian probabilities closer to .50 indicate more difficult dichotomous choices, as categorized in Reference ¹⁵).