Hi everyone,

I had to submit my homework online and one of the questions were...

Is it mutually exclusive if you were to roll a die and get a number greater than 3, and get a number less than 3?

I put it was not mutually exclusive. I got it wrong though. I thought events were mutually exlcusive when they can occur at the same time. So in this case wouldn't it be not mutually exclusive considering I could not roll a number less than three and greater than three at the same time?

It is, and this will explain it better than I can.

Mutually exclusive events - Wikipedia, the free encyclopedia

Mutual Exclusivity (Mutual Exclusion?) for two events is that one event occurs, but not both. In other words, if you shake two dice, the dies are independent. If one die rolls a number greater than three, there is nothing stopping the second die from also rolling a number greater than 3. The events are not mutually exclusive.

However, on ONE die, it is impossible to throw a number greater than 3 and (in the same throw) a number less than 3. Therefore, the two outcomes ARE mutually exclusive. In two throws, however, the events are independent and, therefore, NOT mutually exclusive.