A local microbrewery believes it produces the best tasting dark beer in Baltimore. To make its case, 7 volunteers are asked to participate in a beer-tasting contest. Each volunteer is asked to taste 5 dark beers; one is the microbrewery's; the other 4 are national favorites. They are then asked to pick the one that she / he prefers. When answering the questions below, assume there is no taste preference for any of the beers (chance alone determines each selection). (Hint: you will be using the binomial distribution to answer these questions)
A) What is the probability that all 7 volunteers pick the microbrewery's beer?
B) What is the probability that exactly 3 of the volunteers pick the microbrewery's beer?
C) What is the probability that at least 4 of the volunteers pick the microbrewery's beer?