A large airport handles 350 pieces of luggage for a particular flight. Among these pieces, 50 of the pieces of luggage are locked. Suppose that 10 pieces of luggage are chosen at random for inspection. a. What is the actual (exact) probability distribution of the number of pieces of luggage selected for inspection that are locked. Give the name of the distribution and the value of the parameters (or you may simply give the formula for p(x)). b. Let Li represent the event that the ith selected piece of luggage is locked. Determine and . Strictly speaking, are the events L1 and L2 independent? c. Note that the population size is much larger than the sample size. What distribution can be used to find approximate probabilities for the number of locked pieces of luggage in the sample? Give the name of the distribution and the value of the parameters (or you may simply give the formula for p(x)). d. Using the approximate distribution, determine the probability that there are exactly 2 pieces of locked luggage in the sample. (Note that the probability using the exact distribution is 0.272.)