Dear all,
My colleagues and I have a probability question regarding computer-aided assessment.
In the computer-based tests used here students typically have to complete 5 questions.
For each question, the computer randomly selects from a bank of 10 alternatives (i.e. 10 different altneratives for each of the five questions).
We have worked out (using the geometric distribution) that if the test only contained one question (with 10 possible alternatives), the students would, on average have to complete 29 (29.3) tests in order to obtain a copy of all the 10 possible questions.
Using simulation, we have also worked out that if the test had 2, 3, 4, 5 questions the students would have to access the following number of tests in order to obtain a copy of all the 20, 30, 40, 50 (respective) possible questions.
2 questions: 35
3 questions: 39
4 questions: 42
5 questions: 44
What we can't do is to show this theoretically.
If anyone could help us with this, it would save me hours spent puzzling over it! I hope my explanation is clear.
My email address is given below.
Thanks in advance,
Rosie Shier.
Rosie Shier
Mathematics Education Centre
Loughborough University
Loughborough
LE11 3TU
Tel: 01509 227466
Email: [log in to unmask]
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