there are 17 questions on a moodle test, each of which consists of randomly drawing from three possible questions. how many different tests are possible? if two students take the exam, what is the probability that they will take the same exam?

Question

there are 17 questions on a moodle test, each of which consists of randomly drawing from three possible questions. how many  different tests are possible? if two students take the exam, what is the probability that they will take the same exam?

anonymous · Answer

I pretty sure that the number of tests is 3^17 = 129,140,163. I have noooo clue how to approach the problem of probability though...

anonymous · Answer

You're right about the number of tests.

anonymous · Answer

Given that it's arbitrary which questions they choose, call test A (the test that No.1 takes), say that A=(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1) 
Now, we've defined person 1 as choosing (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1), so the prob of that happening is =1.

The probability of person 2 choosing (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1) , however, is 1/(129,140,163), as there are 129,140,163-1 different tests they could have chosen

anonymous · Answer

do you mean 1/129,140,162? and that is the probability of persons 1 & 2 getting the same test? or do i have to multiply the probabilities for persons 1 & 2 together for that?

anonymous · Answer

That is the probability, yes. I have already multiplied them together, as the prob of person 1 getting the same test as person 1 is 100%

anonymous · Answer

1/129,140,162 is the probability of them getting the same test then? Okay, I'll take your word for it. I have a really really hard time wrapping my mind around these types of questions and the associated math, they never seem to make a lot of sense to me. Thanks for your help! ^_^

anonymous · Answer

OK. The key thing is that it's irrelevant WHICH test the first person chooses, just that the 2nd person's choice matches the 1st's