MATH 381, Discrete Distribution Practice 1. A group of college students includes 3 seniors, 4 juniors, and 7 freshmen. A group of 6 students is selected randomly. What is the probability that this group includes exactly 3 freshmen? . 2. You randomly select 5 cards from a deck. What is the probability that you select exactly 2 kings? 3. A biased coin has P(heads) = .7. (a) If the coin is tossed 8 times, what is the probability of tossing exactly 2 heads? More than 2 heads? What is the expected number of heads in 8 tosses? (b) What is the probability that the coin must be tossed 8 times to obtain exactly 2 heads? What is the expected number of tosses required to observe exactly 2 heads? 4. What is more likely: exactly 5 heads in 10 tosses of a fair coin; or exactly 10 heads in 20 tosses of a fair coin? Or are the probabilities the same? Explain your answer. 5. There are 10 multiple choice questions on a test. Each question'has 5 answers to select from. If a student is guessing randomly, what is the probability that the student will guess 6 or more answers correctly? 6. Roll 2 dice. What is the probability that 10 rolls are required to observe 2 sums of 7? What is the expected number of rolls needed to observe exactly 2 sums of 7? 7. Twelve trial jurors are randomly selected from a population which consists of 45% Latin X citizens. Of the 12 jurors selected, 2 are Latin X. (a) What proportion on this jury is Latin X? (b) What is the expected number of Latin X people in a randomly selected jury of 12 people from the population described? (c) What is the probability that there would be 2 or fewer Latin X individuals in a randomly selected jury of 12 people? (d) What might you conclude about the jury selection process that resulted in 2 Latin & people