2. Eight students have applied for the merit scholarship. This year 4 merit scholarships were awarded. If a random sample of 2 applications (from the population of eight) is selected, (a) What is the probability that 2 were the recipient of the scholarship? (b) What is the probability that none were the recipients of the scholarship? 3. Ten percent of the parts produced by a machine are defective. Twenty parts are selected. Define the random variable x to be the number of defective parts. (Use Formulas and show work!!) (a) What is the probability that exactly 3 parts will be defective? (b) What is the probability that the number of defective parts will be 5? (c) What is the expected number of defective parts? (d) What is the variance for the number of defective parts