A multiple-choice test consists of eight questions and three answers to each question (of which only one is correct). If a student answers each question by rolling a balanced die and checking the first answer if he gets 1 or 2, the second answer if he gets 3 or 4, and the third answer if he gets 5 or 6, what is the probability that he will get exactly four correct answers?
This is a pretty straightforward binomial question, the probability of success (ie, getting one question correct) is given by 1/3, then we can directly plug it into the binomial probability distribution function to obtain the probabilities, however I'm wondering how the question would change if it was stated like this:
What if he chooses the second answer if he gets a 3 or 4 or 5, chooses the first answer if he gets a 1 or 2 and chooses answer 3 if he gets a 6?
How would I work out the probability of getting one question correct now?