Homework: Discrete Structures Module
For all the problems show your work. Giving only the correct answer is insufficient for getting the full credit.
A. Solve the following problems using the multiplication principle for counting.
1. I have 8 flavors of ice cream and 4 different toppings. How many different ice cream sundaes can I make if I choose one flavor of ice cream and only one topping?
2. A restaurant is preparing a prix fixe menu that has 4 choices of appetizers, 2 soups, 7 entrees and 4 desserts. How many different dinners can be made from the menu? Assume that each guest chooses one of each dish.
3. How many different ways can I rearrange the letters in the word COMPUTER?
4. How many 4-letter "words" can I make from the letters of the word COMPUTER? You can re-use letters. For example CCCC, UPCT, etc..
5. How many 3-letter "words" can I make from the letters in COMPUTER -? This time you cannot re-use letters. For example COM, POT, PUT, etc..
B. I have a bag of marbles with 5 yellow marbles, 11 red marbles and 7 brown marbles. Two marbles are drawn at random. First, draw the tree diagram and then compute the following probabilities - give your answers in fractions, in lowest terms.
With the aid of the probability tree, find the probability of:
1. choosing 2 red marbles.
2. Choosing two marbles of the same color.
3. Choosing different colored marbles.
C. We are studying the success rate of newly opened hotel-casinos in Las Vegas. We measure that (a) 65% of these hotel-casinos generate positive revenue from the gambling business (i.e. the casino), and (b) 45% generate positive revenue from the hospitality business (i.e. the hotel). We are also told that 20% of these hotel-casinos are profitable in both gambling and hospitality.
1. What percentage of the newly opened hotel casinos generate positive revenue either from gambling or from hospitality?
2. What percentage of the newly opened hotel casinos generate positive revenue neither from gambling nor from hospitality?
D. 87% of the people who buy a gas grill are male, and 69% and homeowners. Assuming that the percentage of the buyers that are male homeowners is 59%, what fraction of the buyers either male or homeowners.
E. You make 40% of the basketball shots you take. What is the probability you make exactly 7 out of 12 shots?
Format your homework according to the give formatting requirements:
1. The answer must be double spaced, typed, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the homework, the course title, the student's name, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The references and Citations should follow APA format. The reference page is not included in the required page length.