are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select five peanut M&M’s from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.) (a) Compute the probability that exactly two of the five M&M’s are blue. (b) Compute the probability that two or three of the five M&M’s are blue. (c) Compute the probability that at most two of the five M&M’s are blue. (d) Compute the probability that at least two of the five M&M’s are blue.

A firm making production plans believes there is a 30% probability the price will be $10, a 50% probability the price will be $15, and a 20% probability the price will be $20. The manager must decide whether to produce 6,000 units of output (A), 8,000 units (B) or 10,000 units (C). The following table shows 9 possible outcomes depending on the output chosen and the actual price.    Production Profit (Loss) when price is $10 $15 $20 6,000 (A) −$200 $400 $1,000 8,000 (B) −$400 $600 $1,600 10,000 (C) −$1,000 $800 $3,000   What is the variance if 6,000 units are produced?

You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $48 or $60 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur.   On the following table, indicate the price paid by the winning bidder. Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) $48 $48 $48 0.125      $48 $48 $60 0.125      $48 $60 $48 0.125      $48 $60 $60 0.125      $60 $48 $48 0.125      $60 $48 $60 0.125      $60 $60 $48 0.125      $60 $60 $60 0.125        The expected price paid is ______   .   Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders would not be willing to bid against each other. The probabilities of the…

If the probability that the Islanders will beat the Rangers in a game is 81%, what is the probability that the Islanders will win at least three out of five games in a series against the Rangers? Round your answer to the nearest thousandth.