Sam Ruggerio operates a fleet of two fishing trawlers. Based on past frequencies, each trawler is 50% likely to bring back 10 tons of fish on a given day, 20% likely to bring back 20 tons of fish, and 30% likely to return empty. Assume the trawlers perform independently.
a. On a randomly selected day, how likely is it that the total day’s catch is 40 tons?
b. If we define a random variable that measures the total day’s catch for Sam’s feet, what are the possible values for the random variable?
c. Show the full probability distribution for the “total day’s catch” random variable.