In robotics applications, few-shot segmentation is crucial because it allows robots to perform complex tasks with minimal training data, facilitating their adaptation to diverse, real-world environments. However, pixel-level annotations of even small amount of images is highly time-consuming and costly. In this paper, we present a novel few-shot binary segmentation method based on bounding-box annotations instead of pixel-level labels. We introduce, ProMi, an efficient prototype-mixture-based method that treats the background class as a mixture of distributions. Our approach is simple, training-free, and effective, accommodating coarse annotations with ease. Compared to existing baselines, ProMi achieves the best results across different datasets with significant gains, demonstrating its effectiveness. Furthermore, we present qualitative experiments tailored to real-world mobile robot tasks, demonstrating the applicability of our approach in such scenarios. Our code: https://github.com/ThalesGroup/promi.