Mathata is a student taking a course in statistics. Unfortunately, Mathata is not a good student. Mathata does not read the textbook before class, does not do homework, and regularly misses class. Mathata intends to rely on luck to pass the next quiz. The quiz consists of 10 multiple-choice questions. Each question has five possible answers, only one of which is correct. Mathata plans to guess the answer to each question.

a)Define clearly the random variable X in this problem. Hence, fully state the probability mass function for X, indicating the support of X.

b)What is the probability that Mathata gets no answer correct?

Find the probability that Mathata fails the quiz if the pass mark is 50%