I believe that we do not know anything for certain, but everything probably.
Christiaan Huygens, Oeuvres Completes

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Probability Theory

Probability theory grew out of the study of chance processes, particularly those related to gambling. Its applications now are very broad. In particular, probability theory provides the foundation for statistical practice.

There are various ideas about what probability means. Two common interpretations are these:
  1. Frequentist: If a random process is repeated many times, the probability of a particular outcome can be thought of as the proportion of times that outcome occurs.

  2. Classical If all outcomes of a random process are equally likely, the probability of a particular outcome is the number of times that outcome can occur divided by the number of possible outcomes.

If the student guesses, all choices are equally likely. Based on the classical interpretation of probability: there is one correct choice out of 5 total choices so the probability of guessing the correct answer is 1/5.