On my exam my teacher isn't going going to state what type of problem it is. He is going to put questions based on probability, independent-dependent events, mutually/non mutually events, pemutations and combinations. These questions are all going to be mixed up and I have trouble identifying the type of problem it is. I understand what they mean but its hard for me to find out a way to answer the problem when I don't know the type of problem it is. So if you know an easy way to quickly identify a problem, that will be greatly appreciated thanks

Well, I'll try.

The difference between a permutation and a combination is if order matters. For instance, is ABC and BAC the same thing? If it's something like a combination lock, then it's not the same thing and therefore order matters. (i.e. the order it's in makes a difference) That's a permutation. But if that is three people you are picking from a crowd, it won't matter what order you pick them in - you'll still have the same 3 people. So order doesn't matter. That's a combination. If, however, you are putting those people into specific slots, like say president, VP, etc, then it becomes a permutation cause the order now does matter. Think of putting the picks into "slots." Does it matter which slot it goes into? Random people or the lottery, no it doesn't. License plate or combination lock or people into positions, yes it does.

Neither of those are a probability. Those are used to figure out how many ways there are to do something. The tricky part is also that just cause you need to know how many ways there are, it's not necessarily either of those. They are both used in a case where you are picking from a pool, and as you pick, that one can't be used again, so the number in the pool drops by one each time you pick. For instance, if you're picking 3 people out of 10, or you're picking off a deck of cards, once you pick one, it's out of the pool. If you can't repeat a number or letter, then it's out of the pool too.

If you can repeat one, that isn't a permutation or combination either one. Then you have to use your multiplication rule. So like a combination lock where you can repeat numbers - you can pick from the same pool again. (Like 10 x 10 x 10.) Or, if you move to a different pool... Say picking from two kinds of bread, then from three kinds of meat, then from two condiments -- you aren't picking from "a" pool. You're changing pools each time. That's just straight multiplication (2 x 3 x 2). Those aren't combinations or permutations at all.

As for independence vs dependence. Being dependent means that the probability of one thing happening depends upon whether something else has already happened or not. Independent means that one thing already happening does not affect the outcome of another thing. Great example of independent is dice or coins. It doesn't matter what you got the first time you toss it - the probability remains the same for each subsequent throw. (Getting heads really has the same probability even if you've already gotten heads 50 times in a row. :-))

Dependence is used with conditional probabilities. You set some condition that exists first, and then test whether that condition changes the probability of something else. For instance, what's the probability that someone at your school has to take statistics? Let's combine that with what division they are in and you also have probabilities of whether they are in the business division, fine arts, etc. If you already know someone is in the business division, what does that do to the probability they have to take statistics? Increases it. If you don't know what division they are in, it's just the overall probability. If you already know what division they are in (the condition), then it would change the probability. That means those events (division and have to take statitics) are dependent.

Mutually inclusive is when the two events cannot both happen. Like you can own both a computer and a TV. There's a crossover there. So that's not mutually inclusive. But you cannot both drive to school and take the bus to school. So those events are mutually exclusive. (And don't start getting creative that you can drive to the bus stop and then take the bus!)

Just as a note, contrary to what most people think cause it "feels funny," events that are independent are NOT mutually exclusive. If something is mutually exclusive, they are dependent. If your only choices are driving to school or taking the bus to school, and the probability of driving is .75, if you take the bus, the probability of driving becomes 0. The condition (that you took the bus) changed it and therefore they are dependent on each other. Mutually exclusive events are always dependent events.

Since you seem to be more concerned with how to identify them rather than how to do them, I won't go into equations and such.

I hope I wasn't just repeating what you already know. I'm sure someone can come up with more examples, or you can post certain ones you had trouble with and someone can explain why it is what it is.

Lengthy, me? Never!

Your post is lengthy. Wait... that makes around 800 words! That's nearly the same length as my GP essays! (We are asked to do between 800 and 1000 words and GP can be called English).

I'd rather write a lenthy post than an essay any day. If it was an essay, I'd manage about 100 words if I was lucky. LOL.