The manager of Sam’s Food Mart guarantees that none of his cartons containing a dozen eggs will contain more than one bad egg, despite the fact that 4% of individual eggs are known to be bad. Define the random variable x to be the number of bad eggs observed in a carton containing 12 eggs.
a) Explain why this experiment can be classified as a binomial experiment. Give two specific reasons.
b) Find the probability that a randomly selected carton will contain no bad eggs.
c) If a carton contains more than one bad egg, the manager will replace the entire dozen and allow the customer to keep the original eggs. Find the probability that the manager will have to replace a randomly selected carton of eggs.