The present study aimed at analyzing the performance of Ss at various age levels in a two-choice task, and comparing these findings with those of other investigators who have utilized analogous tasks. 126 Ss, who were 4, 6, 10 or 20 years old, participated in the experiment. A procedure like Weir-type (1964) probabilistic experiment was undertaken. Two different reinforcement percentages for the payoff knob were used, 70% and 100%. Then on a 70% task a marble was delivered on 70 %oftheSs, choices6fthepayoffknob, andthen the 100% task was analogous to a so-called concept attainment task. The main point, which was different from the previous probabilistic problem-solving experiment, was the shift learning design employed. Hence initial payoff associated with a knob in the first session switched to the other knob in the second session just after reaching the problemsolving criterion. Considering both shift design and reinforcement percentages, three conditions were constructed as follows (1) C-1: 100%task (1st session) →70% task (2nd session). (2) C-2: 70% task (1st session) →70% task (2nd session). (3) C-3: 70% task (1st session) →100% task (2nd session). Then authors intended (1) to examine the previously affirmed findings such as U shaped or inverted U shaped relationship between age and some dependent variables by using other variables, and (2) to investigate effects of reinforcement shift on the block-1 of the second session, and then (3) to suggest a possibility of an alternative of view. Obtained results were as follows; (1) In comparison with adults and younger children, middle aged Ss found it significantly difficult to achibve the 70% task in the first session (TABLE 1). (2) In line with (1), middle aged Ss were significantly slow to attain the problem-solving crite rion (TABLE 2). (3) Trend analysis affirmed an inverted U shaped relationship between age and number of trials to the criterion in the first session (TABLE 3 and 4). (4) Mean % correct responses made during the block-5 in the second session were lower in middle aged Ss than in adults and younger children. Trend analysis for this dependent variable showed a U shaped relationship between age and mean % correct responses (TABLE 6, 7 and 8). (5) Middle aged Ss made more simple pattern responses during the second session (TABLE 9). (6) In every condition, younger children made quite a few correct responses and pattern responses during the block-1, then showed a strong tendency of perseverative responses to the initially reinforced position (TABLE 10 and 11, Fig. 1). Most of the findings were parallel with those of Weir (1964). However the authors' concern is the fact that younger children showed not only reward maximization, but also strong perseverative response tendency in the initial block of the 2nd session. Hence in order to integrate these somewhat inconsistent results, the authors attempted to introduce mathematical set theory and then discuss previous findings and the present results in terms of following hypotheses: (1) Younger children could attend to the dominant cue set associated with reinforcement, but neglect the other cues (i, e., complementary set) and the mutually exclusive rule between these cue sets.(2) Instead, adults and older children could logically operate these cue sets and the set relation defined by set theory (e. g., exclusion rule between set and complementary set.)