For the given decision algorithm, find how many outcomes are possible.

Step 1 Step 2

• Alternative 1: 1 outcomes Alternative 1: 3 outcomes
• Alternative 2: 4 outcomes Alternative 2: 4 outcomes Alternative 3: 1 outcomes

2. Your broker has suggested that you diversify your investments by splitting your portfolio among mutual funds, municipal bond funds, stocks, and precious metals. She suggests five good mutual funds, five municipal bond funds, six stocks, and three precious metals (gold, silver, and platinum).

(a) Assuming your portfolio is to contain one of each type of investment, how many different portfolios are possible? choices

b) Assuming your portfolio is to contain four mutual funds, four municipal bond funds, one stock, and two precious metals, how many different portfolios are possible? choices

3. A company assigns to each of its employees an ID code that consists ofone or twouppercase letters followed by a digit from 0 through 9. How many employee codes does the company have available? employee codes

4. The "Dogs of the Dow" are the stocks listed on the Dow with the highest dividend yield. The following table shows the top 10 stocks of the "Dogs of the Dow" list for 2015, based on their performance the preceding year.

Symbol	Company	Price ($)	Yield
T	AT&T	33.59	5.48%
VZ	Verizon	46.78	4.70%
CVX	Chevron	112.18	3.82%
MCD	McDonald's	93.70	3.63%
PFE	Pfizer	31.15	3.60%
GE	General Electric	25.27	3.48%
MRK	Merck	56.79	3.17%
CAT	Caterpillar	91.53	3.06%
XOM	ExxonMobil	92.45	2.99%
KO	Coca-Cola	42.22	2.89%

You decide to make a small portfolio consisting of a collection of 6 of the top 10 Dogs of the Dow.

(a)How many portfolios are possible? portfolios

(b)How many of these portfolios contain MRK but not PFE? portfolios

(c)How many of these portfolios contain at most one stock priced above $60? portfolios

5 .Elimination Tournaments In an elimination tournament the teams are arranged in opponent pairs for the first round, and the winner of each round goes on to the next round until the champion emerges. The following diagram illustrates a 16-team tournament bracket, in which the 16 participating teams are arranged on the left under Round 1 and the winners of each round are added as the tournament progresses. The top team in each game is considered the "home" team, so the top-to-bottom order matters.A tournament bracket has four rounds. Starting with the round in the leftmost column and moving right, the rounds are as follows.

• Round 1 has sixteen entries organized into pairs. Each pair leads to a single entry in round 2.
• Round 2 (quarter final) has eight entries organized into pairs. Each pair leads to a single entry in round 3.
• Round 3 (semifinal) has four entries organized into pairs. Each pair leads to a single entry in round 4.
• Round 4 (final) has a single pair of entries. The pair leads to a single entry labeled "champion."

To seed a tournament means to select which teams will play each other in the first round according to their preliminary ranking. For instance, in professional tennis and NCAA basketball the seeding is set up in the following order based on the preliminary rankings: 1 versus 16, 8 versus 9, 5 versus 12, 4 versus 13, 6 versus 11, 3 versus 14, 7 versus 10, and 2 versus 15.? This exercise is based on various types of elimination tournaments. (Leave each answer as a formula. Do not enter your answers using the notation P(n, r), or C(n, r).) (a)How many different seedings of a 16-team tournament are possible? seedings

(b)In how many seedings will the top-ranked team play the bottom-ranked team, the second-ranked team play the second-lowest-ranked team, and so on? seedings

6. This exercise is based on the following list of top DVD rentals (based on revenue) for the weekend ending November 6, 2011.

Title	Rank
Captain America: The First Avenger	1
Bad Teacher	2
Fast Five	3
Cars 2	4
Trespass	5
Bridesmaids	6
Zookeeper	7
Transformers: Dark of the Moon	8
Scream	9
Thor	10

Rather than studying for math, you and your buddies decide to get together for a marathon movie-watching, popcorn-guzzling event on Saturday night. You decide to watch five movies selected at random from the above list.

a) How many sets of five movies are possible? sets

(b)Your best friends, the Lara twins, refuse to see Bridesmaids and also insist that at least one of Captain America or Thor be among the movies selected. How many of the possible groups of five will satisfy the twins? groups

7. President Barack H. Obama's cabinet consisted of the Secretaries of Agriculture, Commerce, Defense, Education, Energy, Health and Human Services, Homeland Security, Housing and Urban Development, Interior, Labor, State, Transportation, Treasury, Veterans Affairs, and the Attorney General.? Assuming that President Obama had 25 candidates, including Hillary Clinton, to fill these posts (and wished to assign no one to more than one post), complete the following sentences.

(a) The sample space is the set of all lists of people chosen from

(b) The event that Hillary Clinton is the Secretary of State is the set of all lists of 15 people chosen from

8 Is the following true or false? Every sample space S is a finite set.

Explain.

The sample space is a specified subset of all possible outcomes.

The sample space contains only a predetermined number of favorable outcomes.

We cannot determine which outcomes are possible until they are observed to occur.

When conducting an experiment we must be able to list all possible outcomes before conducting the experiment.

Some experiments may have no definite end, such as observing the number of coin flips until heads occurs.

9. The map below shows the percentage change in housing prices from June 2014 to June 2015 in each of nine regions (U.S. Census divisions).?

New England 3.18 West Middle North East Atlantic Mountain Central North 1.72 7.17 3.91 Central 4.51 Pacific 7.68 East South South Atlantic West Central 6.12 South 4.88 Central 6.92New England 3.18 West Middle North East Atlantic Mountain Central North 1.72 7.17 3.91 Central 4.51 Pacific 7.68 East South South Atlantic West Central 6.12 South 4.88 Central 6.92