You're taking the final exam for your Introduction to Probability and Statistics course, and once again you've failed to study (you were up all night solving online brainteasers).
The exam is multiple choice. It asks 120 questions, each of which has possible answers A, B, and C. You haven't the faintest idea how to answer any of the questions and so you turn to your old standby strategy: always answer B.
As quickly as you can, you fill out all the B's on your exam paper.
Shortly after you've finished, your professor gets up at the front of the class and announces that an error was made while printing the exam: answer C should not appear on the answer sheet because C is not the correct answer to any question.
You now have several options:
- leave your answers as B
- switch your answers from B to A
- switch some, but not all, of your answers from B to A
Given your goal is to get as many answers correct as possible, what strategy do you use, and how many correct answers do you expect to get (on average) when using this strategy?
Puzzlers are politely encouraged to place answers in spoiler blocks to avoid inadvertently spoiling the fun for other readers. :)