Probability/ Student, points

Hi to all!
I don`t know to do this problems (they are from my last exam), so I would much apriciate if someone can help

1) The student fills IQ test (true - false based).There is m offered answers on each of N questions. For every question student knows the answer (with probability P) or answering by random (with probability 1-P), and his answer is correct with the probability of 1/m.

a) Determine the probability that the student really knew the answer to the first question, if we know that he gave a correct answer.
b) Determine the probability that the student will complete correctly the entire test.

2) Two points are randomly selected (M1 and M2) along the line L (L => 1). Determine the probability that the M1M2 <1?

Desperately need help :(

Look up Bayes theorem. And consider how to answer the similar following question

On average about P% people have an ailment (which cannot be easily detecting by just looking at them)
There's a test that can be used but doesn't always get the answer correct.
If the person does have the ailment the chances of detection is (say) 98%
If the person doesn't have the ailment the chances of a false positive (i.e. incorrectly stating they have the ailment) is (say) 5%.

What you know is that the test says the patient HAS the ailment and the question is what are the chances the patient actually does.

Consider the chances that the patient DOES and the test was correct against the patient DOESN'T and the test was wrong.

I found mistae in first problem...it should be like this:
1) The student fills IQ test (he marks he answers by putting an circle over the correct answer).There is m offered answers on each of N questions. For every question student knows the answer (with probability P) or answering by random (with probability 1-P), and his answer is correct with the probability of 1/m.

a) Determine the probability that the student really knew the answer to the first question, if we know that he gave a correct answer.
b) Determine the probability that the student will complete correctly the entire test.

There is probably also a problem in the 2nd question, because if L >=1, the probability that M1 * M2 < 1 = 0.

Quote: dwheatley

There is probably also a problem in the 2nd question, because if L >=1, the probability that M1 * M2 < 1 = 0.

Maybe there is not a problem; maybe it is just a logic question. It's almost like asking "If you roll two 6 sided die, what is the probability you will will have a total of 13 or greater?"

It should be like that. L is somite (cut off) and it`s greater or equal to 1.
and M1M2 is line, like point M1 to point M2.

Or, let it be like this:
1.........2.........3...........4............5
|----------|----------|------------|-------------|.... this i L
On it, we need to put 2 points M1 and M2, so that M1M2<1...and what is probability for that?

Although I haven't really looked at the second question, here's my effort.

Initially I had thought that one chose two values for M1 and M2 where both are strictly less than L but greater than 0 - and work out the chances of the product being < 1 - this presumably has an answer based on L (and obvious L has to exceed 1 for there to be any chance).

Now you mention it, it seems that there is a line, like an X-axis, and goes from 0 to L "(0,L)", "[0,L)" etc. where L > 1 (if L<=1 then it's impossible) and that M1 was a random point and M2 was another random point. The question is how often the length of the line M1 M2 is less than 1. This seems quite a reasonable question as the answer would be a formula, presumably via integration of some sort, based solely on the value of "L".

Quote: Sheldon

I found mistae in first problem...it should be like this:
1) The student fills IQ test (he marks he answers by putting an circle over the correct answer).There is m offered answers on each of N questions. For every question student knows the answer (with probability P) or answering by random (with probability 1-P), and his answer is correct with the probability of 1/m.

a) Determine the probability that the student really knew the answer to the first question, if we know that he gave a correct answer.
b) Determine the probability that the student will complete correctly the entire test.

For a) read the enounce like this:"The student fills IQ test. There is m offered answers on each of N questions". Now jump to the end of the enounce "......his answer is correct with the probability of 1/m"

Now you know he gave a correct answer, this event had m possible cases, out of which p are favorable to the fact that he " knows the answer". So then, P(student really knew the answer given he gave a correct answer) = p/m, i think ......