1. If we throwing a coin and a die list the sample space (1 point) 2. Out of 5 Mathematician and 7 Statistician a committee consisting of 2 Mathematician and 3 Statistician is to be formed. In how many ways this can be done if (1poin each) a. There is no restriction b. One particular Statistician should be included c. Two particular Mathematicians cannot be included on the committee 3. Suppose that an examination consists of six true and false questions, and assume that a student has no knowledge of the subject matter. The probability that the student will guess the correct answer to the first question is 30%. Likewise, the probability of guessing each of the remaining questions correctly is also 30%. (2point) a) What is the probability of getting more than three correct answers? b) What is the probability of getting at least two correct answers? c) What is the probability of getting at most three correct answers? d) What is the probability of getting less than five correct answers? 4. Two dice are rolled. Let X be a random variable denoting the sum of the numbers on the two dice.(3point). i) Give the probability distribution of X ii) Compute the expected value of X and its variance​