Let's consider the phrasesat 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 problem with probability calculations.

Consider the following statement: Mary (spendsat least, spendsat most,spendsless than, spendsmore than) 20 minutes per day exercising. Depending on which phrase you chose in parenthesis you end up with a different expression and meaning. When speaking of probability,P(x20)

P(x20)(probability that Mary spendsat most20 minutes exercising) means something different fromP(x>20)

P(x>20)(probability that Mary spendsmore than20 minutes exercising).

Write an expression related to your major foreachof 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.