Today in Prob/Stats we were continuing work with the binomial random variable. What would be the average number you would expect to get correct on a 10 question multiple quiz with 4 answers each? Since you are guessing, the probability of getting a correct answer is 0.25. The average number correct is 1/4 of 10 or 2.5. Although this calculation makes sense, I had a feeling my students weren't buying it. So, I changed my lesson.
I decided to have students take a mock quiz. Try it with your students. It's quite fun, actually. Tell them to number their paper from 1-10 and write down answer choices of A, B, C or D beside each question. As they do this, you make up an answer key. Next, have students check their own work as you read the answer key. I had students hold up their fingers to show how many they got correct and quickly totaled 33 total correct out of 13 students or an average of 2.54. One student got them all wrong and one student got 5 correct. After that we calculated the binomial probabilities for 0 correct and 5 correct. These probabilities and the mean of 2.5 for this binomial distribution made more sense after this mid-lesson change.