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Ignoring the role of chance in science distorts the nature of the scientific process. Teachers can address this issue by means of several in-depth historical case studies, such as the discovery of electromagnetism by Oersted. Oersted was led to his lecture experiment by logic (two new hypotheses), but its success from the first trial was largely due to chance. Reproducing Oersted's experiment in the classroom complements the story by allowing students to see for themselves the role of some accidental factors, such as the choice of materials and instruments. The message to students is that chance and logic go together in science.