Picking variables

[Halo3]

If a question asks something that requires plugging 2 (or any number) of variables ex. - "what is the product of x and y"

x and y can be the same thing right (ex. x and y can both be 1)? unless they say "x and y are distinct" or "x and y are mutually exclusive"?

[rfernandez]

Yes, you are correct. The "default setting" is that any variable can take on any value, including the possibility that two variables have the same value. The problem must explicitly state it if the two variables may not be equal, such as in "if x and y are two different prime numbers..."

By the way "mutually exclusive" is used in probability to describe two events that cannot occur at the same time. For example, "rolling a 3" on a die and "rolling an even number" are mutually exclusive because the two events have essentially nothing in common. Compare this to the events "draw a queen" from a deck of cards to "draw a black card." Clearly, these events are not mutually exclusive because it's possible for both events to occur simultaneously, namely by drawing the queen of spades or the queen of clubs.

Linking this to your question, it is possible for two mutually exclusive events to have the SAME probability, so be careful not to make an assumption that the VALUES must be different. For example, consider the mutually exclusive events "roll an even number" on a die and "roll an odd number." Although the events are mutually exclusive, their probabilities are equal, namely 1/2.