So i guess this is the forum where i should post this . If any1 wants to help me please explain how to solve this ( i got a exam in like a week and i would like to know how to solve this )

A multiple choice examination has 25 questions, each with 5 possible answers,
only one of which is correct. Suppose that one of the students who takes the examination answers each of the question with an independent random guess.
a) Write the random variable representing the number of correct answers.
b) Which is the expected number of correct answers?

I'm bad at math, but if I'm not mistaken, isn't b) an obvious 5/25 or 20%?

These forums would be more appropriate for your question:

http://forumserver.twoplustwo.com/25/probability/
http://forumserver.twoplustwo.com/47...th-philosophy/

To answer your question, 1/5 = 20% is the chance of guessing correctly any one question. This means (1/5)*25 = 5 questions will be correctly guessed on average.

The formulas for this are:

p = 1/m
c = p*n (or c = n/m)

where

p: probability of a given question guessed correctly
c: expected number of correct guesses
m: number of choices per question
n: number of questions

Your calculation coincidentally gets the correct answer for a). For b) it produces a percentage when a number is sought. Your method is incorrect. To see this, consider what would have happened if the number of questions were 100 instead of 25, then your calculation would be 5/100 = 5%, which is clearly wrong. To get an answer for a) the result should be independent of the number of questions i.e. 1/5 = 20%.

If I know that the guy is getting 1/5 questions correct then I'm in no hell going to assume that he is going to get 5/100 correct - no matter how badly I suck at math. Not sure where you got this from but if somebody is purely guessing on a multiple choice quiz where there are always 5 choices for each question and one correct question then their expectation is always going to be 20% unless there is something that I am missing.

He got that impression because you said 5/25, indicating that you thought the problem was solved by (no. of possible answers)/(number of questions). Clearly you wrote 5/25 because you're already aware 20% of 25 is 5 so it was just a way of expressing the answer. If you had wrote 25/5 he wouldn't have posted what he said.

Understandable from both sides.

No.

It was clearly stated 5/25 was his answer to b), but the answer is 5 and not 5/25.

Lol, obviously I'm aware of that. He chose to answer b as a % and not a number, and in doing so he said you'd guess 5 out of 25 right, or 20%. He represented that as 5/25, he obviously wasn't giving an equation he was just saying 5 out of 25.

I'm not arguing that the way he wrote it mathematically is wrong, no doubt about that. He just didn't understand why you thought he would come up with 5% if there were 100 questions. I was telling him that was the case and why he was wrong, even though he had the right answer (and thought process). If OP had 100 questions in his hypothetical, the guy wouldn't have said 5, he just didn't write down his thought process the right way.

Don't be such a nit?

Actually, I managed not to think of the interpretation "5 out of 25." LOL

My remark about 20% being the answer to a) is wrong. 20% is also wrong as an answer for b). The answer to a) is X = {0, 1, 2, ..., 25} where the X_i = the number of correct answers. The answer to b) is 5.