1. A random experiment consists of throwing a triangular shape with three faces three times. The first face has the number 1, the second face has the number 2 and the third face has the letter A.

1. List the sample space of the random experiment.   
2. Assume the faces are equally likely, what is the probability an outcome of experiment has at least one A?                                                                                                  
3. the letter A is three times likely to occur in a throw than the faces that has the numbers and the faces that has the numbers are equally likely. What is the probability an outcome of the experiment has at least one A?  

Suppose that nn independent trials are performed, with trial ii being a success with probability 1/(2i+1).12i1. Let PnPndenote the probability that the total number of successes that result is an odd number.

1.Find Pn for n=1,2,3,4,5.

2.Conjecture a general formula for Pn.

3. Derive a formula for Pn in terms of Pn−1

Verify that your conjecture in part (b) satisfies the recursive formula in part (c). Because the recursive formula has a unique solution, this then proves that your conjecture is correct.

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfil each week is 2.

(a) What is the probability that in a given week the plant cannot fulfil all the placed orders?

(b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

1) Let X be a continuous random variable. What is true about fX(x)fX(x)?
fX(2) is a probability.
fX(2) is a set.
It can only take values between 0 and 1 as input.
fX(2) is a number.

2) Let X be a continuous random variable. What is true about FX(x)FX(x)?
FX(x) is a strictly increasing function.
It decreases to zero as x→∞x→∞.
FX(2) is a probability.
FX(x) can be any real number.

Contracts for two construction jobs are randomly assigned to one or more of three firms A, B, and C. Let Y1 denote the number of contracts assigned to firm A and Y2 the number of contracts assigned to firm B. Recall that each firm can receive 0, 1 or 2 contracts.

(a) Find the joint probability function for Y1 and Y2.

(b) Find the marginal probability of Y1 and Y2.

(c) Are Y1 and Y2 independent? Why?

(d) Find E(Y1 − Y2).

(e) Find Cov(Y1, Y2)

1. Using basic properties of probabilities, state two reasons how you know this information is not accurate.

2. The next interviewer you meet with is excited to show you a dice game he has developed that he is hoping to sell to a local casino. The game involves using two 10 sided dice with faces numbered 1 through 10.

Create a table to show all outcomes of one roll of the dice.

3. Using the same scenario as in number 2, determine the probability of rolling a sum of 11 on the two dice.

4. Using the same scenario as in number 2, determine the probability of rolling at least one 7 on the two dice.

5. Using the same scenario as in number 2, determine the probability of rolling doubles twice in a row.

6. Using the same scenario as in number 2, your interviewer tells you that the game costs $1 to play and it has an expected value of 47 cents for every dollar spent. Use the following payouts to determine the expected value of the game. Do you agree with your co-worker’s assertion?

• Make Excel do all of the necessary calculations
• Report answers on the worksheet
• Label answers as the questions are labelled: a, b, c,…
• Use the probability notation p(A), p(Aand B),… etc
• Submit your spreadsheet in Blackboard Assignment.

2. Due to recent global economic trends, Brazilian currency has lost value compared to the US dollar. This devaluation caused an increase in the price of products in Brazil. The following table summarizes results from a consumer survey that asked about the number of products being purchased and whether the brands purchased had changed (a trend towards purchasing less expensive brands was expected)

What is the probability that a consumer selected at random:

a. purchased fewer products than before?

b. purchased fewer products and changed brands?

c. purchased fewer products or did not change brands?

d. Constance Aguero changed the brands she purchased. What is the probability that she purchased fewer number of products?

e. Robert Nanaim is purchasing fewer products. What is the probability that he has changed brands?

f. Are the events Brands purchased and Number of products purchased independent events?   Show the test.

Some suggest that we have entered into a new era of global protectionism. Develop an argument about why this can be a good thing. What are some trade tools being used today to support protectionism? Who wins and who loses? [This is a Short Answer prompt.]

Identify the mistakes managers typically make in the refreezing part of the change management process.  Check all that apply.

Not systematically planning for and creating short-term wins

Not creating a powerful enough guiding coalition

Not removing obstacles to the new vision

Not anchoring changes in the corporation’s culture

Chuck Stout is the RM for the Holiday Inn Express. His 220-room property normally sells 85 percent of its rooms on Tuesday nights at an ADR of $141.50. All variable costs related to selling his rooms are $55.00 per room. The DOSM at his Holiday Inn Express is proposing to place a bid to sell 125 rooms for a Tuesday night next month at a rate of $109.00 per room. Chuck believes that if the hotel wins this group rooms bid, the transient room sales for that day will ensure a sell-out at the rate of $141.50.

What would be the total amount of after-variable costs rooms’ revenue the hotel will achieve if it wins the group rooms contract?

What would be the after-variable room’s income if the hotel does not win the contract?