How people make decisions under risk remains an as-yet-unresolved but fundamental question. Mainstream theories about risky decision making assume that the core processes involved in reaching a risky decision include weighting each payoff or reward magnitude by its probability and then summing the outcomes. However, recently developed theories question whether payoffs are necessarily weighted by probability when making a risky choice. Using functional connectivity analysis, we aimed to provide neural evidence to answer whether this key assumption of computing expectations holds when making a risky choice. We contrasted a trade-off instruction choice that required participants to integrate probability and payoff information with a preferential choice that did not. Based on the functional connectivity patterns between regions in which activity was detected during both of the decision-making tasks, we classified the regions into two networks. One network includes primarily the left and right lateral prefrontal cortices and posterior parietal cortices, which were found to be related to probability in previous reports, and the other network is composed of the bilateral basal ganglia, which have been implicated in payoff. We also found that connectivity between the payoff network and some regions in the probability network (including the left lateral prefrontal cortices and bilateral inferior parietal lobes) were stronger during the trade-off instruction choice task than during the preferential choice task. This indicates that the functional integration between the probability and payoff networks during preferential choice was not as strong as the integration during trade-off instruction choice. Our results provide neural evidence that the weighting process uniformly predicted by the mainstream theory is unnecessary during preferential choice. Thus, our functional integration findings can provide a new direction for the investigation of the principles of risky decision making.