What do you expect?

What this expected-value puzzle tests

This is a straightforward expected-value question that checks whether you can correctly set up and compute the mean of a non-uniform discrete distribution. It appears simple on the surface but rewards careful attention to the probability weights assigned to each outcome.

To solve it, you identify the outcome space, verify that the probabilities sum to one, and then apply the definition of expected value by weighting each outcome by its probability. The main skill being tested is your ability to work cleanly with fractional probabilities and avoid arithmetic errors under time pressure.

• Probability mass functions and their properties
• Definition and linearity of expectation
• Verifying that probabilities are valid