Children had to choose one of two urns--each comprising beads of winning and losing colours--from which to draw a winning bead. Three experiments, aimed at diagnosing rules of choice and designed without confounding possible rules with each other, were conducted. The level of arithmetic difficulty of the trials was controlled so as not to distort the effects of the constituent variables of proportion. Children aged 4 to 11 first chose by more winning elements and proceeded with age to choices by greater proportion of winning elements. There were some indications of intermediate choices by fewer losing elements and by greater difference between the two colours. Distinguishing correct choices from favourable draws, namely acknowledging the role of chance in producing the outcome and insisting on the right choice, grew with age. Children switched rather early from considering one dimension to two; they combined the quantities of winning and losing elements either additively by difference or, with age, mostly multiplicatively by proportion. Guided playful activities for young children, based on this research, are suggested for fostering acquisition of the basic constituents of the probability concept: uncertainty of outcome, quantification by proportion, and the reverse relation between the chances of complementary events.