Question 575425
 I am an instructor at a high school and just gave a fifty item multiple choice exam (a,b,c,d). Five students who sit together at a table got the same 8 of the 50 questions wrong. What is the probability of that happening? I want to be able to support the fact that I believe they cheated. Thanks! 
---
The probability I give the same answer as you on one question is 1/2
The probability that 6 others give the same answer is (1/2)^6
---
The probability 8 of us give the same answer is (1/2)^7
----
The probability that happens on 8 questions is (1/2)^7^8 = (1/2)^56
----
BUT, if we assume the 8 questions could hardly be answered incorrectly
by anyone taking your class, the probability does not change, but the
reality of the situation would force us to reasses our suspicion.
============================
In other words the theoretical probability does not always tell the
whole story about events.  It only tells us something about RANDOM
events.  
Question: What is the probability your car will follow some particular
car at a particular red light tomorrow morning? Small, right?
But what is the probability you will follow some car? Hugh, right?
------
Recommend: Look beyond the probabilities.
Cheers,
Stan H.