You are taking a test consisting of 10 multiple choice questions. Each ...

You are taking a test consisting of 10 multiple choice questions. Each question has four answers of which only one is correct. you are taking the quiz and answering randomly, without any knowledge of the material you are tested on.
1. What the is probability distribution of x? (Assume the questions are independent and the chance to hit a correct answer on each questions is 1/4) Can you write a formula for P(x)
2. what is the probability that you answer 2 questions correctly? ( I got .0625)
3. What is the probability that you answer at most 5 questions correctly?
4. What is the probability that you answer more than 7 questions correctly?
5. What is the expected number of questions answered correctly?