Probabilities apply not to events in the real world we are familiar with, but to our information about that world at any given moment in time. But students understand "equally likely" to be based not on the recognition that probabilities apply to our information about events, but the recognition that probabilities do not apply to events in the real world we are familiar with. The purpose of this study is to develop principles for teaching "equally likely" based on the recognition of

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... s applying to our information about events in probability education. As a result, we developed principles for teaching "equally likely", which consist of the following levels: 1. We introduce "equally likely" based on a large number of independent identical trials of a random experiment in the physical world. 2. We expand probability mathematically, and teach conditional probability. 3. We make students understand that: • Probabilities apply not to events in the real world we are familiar with, but to our information about that world at any given moment in time. • "Equally likely" is an assumption in a hypothetical world based on the principle of insufficient reason. through problems about Bayesian updating.