Suppose an entree has 4 possible protein, tofu, pork, beef, and shrimp, and each customer will independently order any one of them with probabilities 0.2, 0.4, 0.3, and 0.1, respectively.

When asked for a distribution, please provide the name and parameter values for a standard distribution.

a) If none of the last ten customers has ordered the beef, consider how many additional customers will place order until there are three more orders for the beef.

Find its distribution, expected value, and variance.

b) What is the probability that the next ten orders will include three tofu, four pork, and three beef?

c) If the next forty orders include exactly sixteen tofu, consider how many of the first ten of those orders are for the tofu.

Find its distribution, expected value, and variance.