Probability: 2 students and 1 professor

popo · 2007-10-22 00:24:00

Hi, someone please help me with this problem?

A professor ask a series of question to 2 students, A and B. If the students dont know the answer then they dont answer. If they think they have an answer then they answer.

For any question, A doesnt know if B can answer nor the answer of B (if B can answer). The same for B.

Before the test begins, the probability that an answer of A is good is unknown. The same thing for B.

Now, the test begins. Here is the score-sheet of the 2 students after many many questions:

For A: he has answered to 50 questions, with 40 good answers and 10 wrong. (80% good)
For B: he has answered to 75 questions, with 30 good answers and 45 wrong. ( 40%good)

By some calculus, the professor find that :
1/ The probability that the next answer of A is good is 0.8
2/ The probability that the next answer of B is good is 0.4
Suppose that (1) and (2) are correct.

Now, the professor ask the 2 students one more question. This time, both A and B think they can respond, and by CHANCE they give the same answer.

The question is: what is the probability that this answer, given by both A and B, is a good answer?

Uhmmmm....

I think this probability must line between 0.4 and 0.8 ; maybe (0.4+0.8)/2 = 0.6 ???

Thank you in advance

Popo

mathsyperson · 2007-10-22 00:49:01

For any question, there are 4 possible outcomes:

- A right, B right (0.32)
- A right, B wrong (0.48)
- A wrong, B right (0.08)
- A wrong, B wrong (0.12)

However, for this question where they give the same answer, only the 1st and 4th outcomes are possible.

The probability that they are both right is therefore 0.32 / (0.32 + 0.12) = 8/11 (I think).

popo · 2007-10-22 02:42:32

Hi, Thank you mathsyperson for giving this help. I presented your reasoning to my professor and he said "It seems to me that is correct" . So, many thanks.

But in the same time, he asked me to formalize this reasoning using "conditional probability". I am trying to do this but it's not trivial.

I think, it should be something like this :

P(the answer is correct) = P ( (A = right and B = right ) | knowing that they have done the same answer ).

So, how to formalize this condition?

Thanks

mathsyperson · 2007-10-22 05:51:11

You're almost there already, you just need to say that second bit in terms of A and B.

P(Answer correct) = P(A correct and B correct | (A correct and B correct) or (A wrong and B wrong)).

popo · 2007-10-22 06:01:21

Ah, right !!!

I was looking for expressing the second bit in terms of A and B, as you said, but I wrote it as:

P(Answer correct) = P(A correct and B correct | (A correct and B correct) + (A wrong and B wrong) = 1)

) thus I counld not do anything with it !

Thanks so much mathsyperson You'rs kind !

popo

Math Is Fun Forum

#1 2007-10-22 00:24:00

Probability: 2 students and 1 professor

#2 2007-10-22 00:49:01

Re: Probability: 2 students and 1 professor

#3 2007-10-22 02:42:32

Re: Probability: 2 students and 1 professor

#4 2007-10-22 05:51:11

Re: Probability: 2 students and 1 professor

#5 2007-10-22 06:01:21

Re: Probability: 2 students and 1 professor

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