TABLE 2.

Correct solution and typical incorrect Bayesian strategies with regard to the correct solution “F out of D” in a typical Bayesian reasoning task (according to Gigerenzer and Hoffrage, 1995; Steckelberg et al., 2004; Zhu and Gigerenzer, 2006; Días and Batanero, 2009; Eichler and Böcherer-Linder, 2018; Bruckmaier et al., 2019).

	Probabilities (with b, c, d, etc.)	Frequencies (with A, B, C, etc.)
Correct solution (Bayesian)	k = f/d = b⋅j/(b⋅j + m⋅c)	F out of D = F out of (F + G)
Incorrect Algorithm (Non-Bayesian)
Joint occurrence (Gigerenzer and Hoffrage, 1995)	f = b⋅j = d⋅k	F out of A
Fisherian/Representative thinking/Transposed conditional (Gigerenzer and Hoffrage, 1995; Zhu and Gigerenzer, 2006; Días and Batanero, 2009)	j = f/b	F out of B
Base rate only/Conservatism (Gigerenzer and Hoffrage, 1995; Zhu and Gigerenzer, 2006)	b	B out of A
Evidence only (Zhu and Gigerenzer, 2006)	d = f + g = b⋅j + c⋅m	D out of A = (F + G) out of A
Likelihood substraction (Gigerenzer and Hoffrage, 1995)	j – m = f/b – g/c	(F out of B) – (G out of C)
Pre-Bayes (Steckelberg et al., 2004; Zhu and Gigerenzer, 2006)	Not applicable	B out of D = B out of (F + G)
Correct positive rate/false positive rate (Steckelberg et al., 2004)	j/m	Not applicable