A 10 question multiple choice exam is given and each question has 5 possible answers. A student takes this exam and guesses at every question. What is the probability they get at least 9 questions correct?
Let's first set up the binomial. The general formula is:
With 5 possible answers on each question, this gives the probability of guessing the correct answer
We're only looking at the probability of getting at least 9 questions correct, and so only care about getting 9 questions correct and 10 questions correct. This gives: