standard_description: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
problem_activity: Task
Is there an equilateral triangle $ABC$ so that  $\overline{AB}$ lies on the $x$-axis and $A$, $B$, and $C$ all have integer $x$ and $y$ coordinates?  Explain.


aligns: no