Guessing

Sarah phoned to tell us how hard her bio-chem exam was.  There were 30 multiple choice questions with four possible answers for each.

She asked me to calculate the probability of passing the exam if she guessed at all the questions.

I quickly wrote a simulation.  I simulated 100 exams of 30 questions with a chance of 25% of getting the right answer on any question.

There were no cases in which the results were over 15 correct.

I calculated the number of cases with more than 10 correct answers.  There were 10 cases.  There were 80 cases of more than 5 correct answers.

I realized I could use the binomial probability distribution to calculate the exact values.  The binomial distribution confirmed the results of my simulation.

I developed a graph of the probability of having X of more correct answers in a 30 question exam.

I asked Sarah if she wanted me to email her the graph.  She said, ‘No’.

But she said she didn’t mind me blogging about it.