You are the meat products manager for Gigantic Foods, a large retail supermarket food distributor who is studying the characteristics of its whole chicken product mix. Chickens are purchased from both Free Range Farms and Big Foods Ltd. Free Range Farms produces chickens that are fed with natural grains and grubs in open feeding areas. In their product mix, 10% of the processed chickens weigh less than 3 pounds. Big Foods Ltd. produces chickens in cages using enriched food grains for rapid growth. They note that 20% of their processed chickens weigh less than three pounds. Gigantic Foods purchases 40% of its chickens from Free Range Farms and mixes the products together with no identification of the supplier. Suppose you purchase a chicken that weighs more than three pounds.
What is the probability the chicken came from Free Range Farms? If you purchase 5 chickens, what is the probability that at least 3 came from Free Range Farms?