Recent work has shown that sample-based Minimum Bayes Risk (MBR) decoding outperforms beam search in text-to-text generation tasks, such as machine translation, text summarization, and image captioning. On the other hand, beam search is the current practice for speech-to-text tasks such as automatic speech recognition (ASR) and Speech Translation (ST). Given that MBR decoding is effective in text-to-text generation tasks, it is reasonable to expect it to also be effective for speech-to-text tasks. In this paper, we evaluate MBR decoding for ASR and ST tasks on English and Japanese using Whisper and its derivative models. We observe that the accuracy of MBR decoding outperforms that of beam search in most of the experimental settings we have evaluated. The results show that MBR decoding is a promising method for offline ASR and ST tasks that require high accuracy. The code is available at https://github.com/CyberAgentAILab/mbr-for-asr