Hello I need help with this part of the assignment , please , thank you

Problem(14) (10 points) Consider a random experiment of throwing two fair dice together. Define the following events: A: { You roll a 7} & B: { At least one of the dice shows a 2 } (a) Identify the sample points in the events A, B, An B, AUB, and AC. (b) Find P(A), P(B), P(An B), P(AUB), and P(AC). Problem(15) (12 points) Consider n independent repetitions of the simple success-failure experiment (with success probability p). Let X be the random variable that denotes the number of successes in the n trials. (a) What are the values that the random variable X takes? (b) Write down the expression (the density function of the binomial distribution) P(X = k). (c) (3 points) Show that ER=o P(X = k) = 1? (d) (5 points) Show that the expectation of the random variable X is that E[X] = np. Study Section 7.4 Expected Value and Variance)