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Journal of Undergraduate Research

Keywords

probable frames, probability task, fraction multiplication

College

Physical and Mathematical Sciences

Department

Mathematics

Abstract

When you toss a coin at the start of a football game and call “Heads!” the probability the coin will land “heads-up” is one-half. If the referee does not hear your prediction, he must toss again. The probability the second toss will land heads is again one-half. But what is the probability that both tosses were heads? In the double coin toss, the probability of two heads in a row is one-half times one-half: one-fourth. Although the rule (multiply the probabilities of the two independent events in order to calculate the probability of both events) is simple to carry out, students often have difficulty in recognizing when to apply this problem-solving technique to real-life situations. Because of this difficulty, and because I believe better understanding creates better learners, better teachers, better spiritual beings, and a better society, this research investigated how persons come to understand where and how multiplicative probability accurately describes a given situation.

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