**Q**** 57. Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: a) What is the probability that all three of the selected homes have a security system? **

**b) What is the probability that one of the selected homes have a security system? c) What is the probability that at least one of the selected homes has a security system? d) Are these events dependent or independent?75. Several Years ago, Wendy’s Hamburgers advertised that there are 265 difference ways to order your hamburger. You may choose to have, or omit, any combination of the following on your hamburger: mustard, ketchup, onion, pickle, tomato, relish, mayonnaise, and lettuce. Is the advertisement correct? Show how you arrive at your answer.77. A new chewing gum has been developed that is helpful to those who want to stop smoking. If 60 percent of those people chewing the gum are successful in stopping smoking, what is the probability that in a group of four smokers using the gum at least one quits smoking?**