Robert is writing a test with 20 multiple choice questions, each with 4 possible answers. If he selects his answers by random guessing, how many questions is he expected to answer correctly?
For this problem, the following conditions are all true:
- There are a fixed number of "trials" (20 questions to be precise)
- The probability of getting a question correct is the same for every question (since all questions have 4 answers with only 1 being correct)
- Presumably all questions are independent of each other (since we were not told otherwise in the problem statement)
Since all of these conditions hold true, we can consider this to be a binomial random variable problem.
In this case, since
Robert can expect to get 5 questions correct by random guessing.