Let’s consider the phrases at least, at most, less than, more than. Often when we are looking at probabilities, it is phrases like those which are key to translating a word problem into a probabilistic problem.
Consider the following statement: The probability that Mary (spends at least, spends at most, spends less than, spends more than) 20 minutes per day exercising. Depending on which phrase you chose in parenthesis you end up with a different expression and meaning in terms of probability theory. For instance, LaTeX: P(x\leq 20)P(x≤20)(probability Mary spends at most 20 minutes exercising) means something different from LaTeX: P(x>20)P(x>20)(probability Mary spends more than 20 minutes exercising).
Write an expression related to your major for each of phrases above and label them with the correct mathematical symbol (use my example as a reference, but I encourage creativity here!). Then explain the differences between the four statements i.e., differences between at least, at most, less than, more than.