Math Is Fun Forum

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