1. List the simple events of tossing a coin three times that includes one head.

2. In rolling a die once, A is the event of getting odd numbers outcome. Then define the complement of A.

3. Given P(A) = 0.7, find P(Ā).

4.In rolling a die once, A is the event of getting even numbers and B is the event of getting number 5. Then P(A or B) =

5. In rolling a die twice, A is the event of getting even numbers and B is the event of getting number 5.

a. P(A and B) =

b. P(A or B) =

c. P(A/B) =

d. P(B/A) =

e. Are A and B independent or dependent events?

6. If P(A) = 0.271 and P(B) = 0.34 and P(A and B) = 0, then P(A or B) =

7. If P(A) = 0.271 and P(B) = 0.34 and P(A and B) = 0.095, are A and B independent or dependent events?

8. What is the difference between P(A/B) and P(B/A)?

9. Find the number of different possible routes to select 5 different locations from 9 that are available.

10. Find the number of different ways to arrange the letters in Kooswinarsinindyah.

11. The chance of a student skip classes on 4^th July weekend is 2 out of 10. What is the probability of asking 10 students and all of them skipping classes on 4^th July weekend?

Neve Commercial Bank is the only bank in the town of​ York, Pennsylvania. On a typical​ Friday, an average of 8 customers per hour arrive at the bank to transact business. There is one teller at the​ bank, and the average time required to transact business is 3 minutes. It is assumed that service times may be described by the negative exponential distribution. A single line would be​ used, and the customer at the front of the line would go to the first available bank teller. If a single teller is​ used:

a) The average time in the line? = ______ minutes?.

b) The average number in the line? = _______customers?.

c) The average time in the system? = _____minutes? .

d) The average number in the system? = ______customers?

e) The probability that the bank is empty? = ____?(round your response to two decimal? places).

f) CEO Benjamin Neve is considering adding a second teller? (who would work at the same rate as the? first) to reduce the waiting time for customers. He assumes that this will cut the waiting time in half.

g) If a second teller is? added, the average time a customer spends in the queue? = ____ minutes?

h) If a second teller is? added, the average number of customers in the queue? =??____ customers.

I) If a second teller is? added, the average time a customer spends in the system? = _____minutes

j) If a second teller is? added, the average number of customers in the system? =?? customers?

2. In the class ic film, Mary Poppins, the Banks children are players in a strategic game with a number of different nannies. In their view of the world nannies are inherently harsh, and playing tricks on nannies is great fun. That is, they view themselves as playing a game in which the nanny moves first, showing herself to be either Harsh or Nice, and the chil dren move second, choosing to be either Good or Mischievous. The nanny prefers to have Good children to take care of but is also inherently harsh, and so she gets her highest payoff of 4 from (Harsh, Good) and her lowest payoff of 1 from (Nice, Mischievous ), with (Nice, Good) yielding 3 and (Harsh, Mischievous) yielding 2. The children similarly most prefer to have a Nice nanny and then to be Mischievous; they get their highest two payoffs when the nanny is Nice (4 if Mischievous; 3 if Good) and their lowes t two payoffs when the nanny is Harsh (2 if Mischievous, 1 if Good).

a. Draw the game tree for this game and find the subgame - perfect equilibrium in the absence of any strategic moves.

b. In the f il m, before the arrival of Mary Poppins, the children write their own ad for a new nanny in which they state: “If you won’t scold and dominate us, we will never give you cause to hate us; we won’t hide your spectacles so you can’t see, put toads in your bed, or pepper in your tea.” Use the tree from part (a) to arg ue that this statement constitutes a promise. What would the outcome of the game be if the children keep their promise?

c. What is the implied threat that goes with the promise in part (b)? Is that implied threat automatically credible? Explain.

d. How cou ld the children make the promise in part (b) credible ?

e. Is the promise in part (b) a compellent or deterrent? Explai n your answer by referring to the status quo in the game – namely, what would happen in the abs ence of the strategic move .   

Edsel Research Labs has $29.60 million in assets. Currently half of these assets are financed with long-term debt at 6 percent and half with common stock having a par value of $10. Ms. Edsel, the Vice President of Finance, wishes to analyze two refinancing plans, one with more debt (D) and one with more equity (E). The company earns a return on assets before interest and taxes of 6 percent. The tax rate is 35 percent.

Under Plan D, a $7.40 million long-term bond would be sold at an interest rate of 12 percent and 740,000 shares of stock would be purchased in the market at $10 per share and retired. Under Plan E, 740,000 shares of stock would be sold at $10 per share and the $7,400,000 in proceeds would be used to reduce long-term debt.

a-1. How would each of these plans affect earnings per share? Consider the current plan and the two new plans. (Round your answers to 2 decimal places.)
  

Earning per Shares

Current ______

Plan D _______

Plan E ________

  
a-2. Which plan(s) would produce the highest EPS? Note that due to tax loss carry-forwards and carry-backs, taxes can be a negative number.
  

• The Current Plan and Plan E

• Plan D

• Plan E

• Current Plan

  
b. Which plan would be most favorable if return on assets increased to 9 percent? Compare the current plan and the two new plans.
  

• Plan D

• Plan Current and D

• Plan E

• Current Plan and Plan D

  
c. Assuming return on assets is back to the original 6 percent, but the interest rate on new debt in Plan D is 8 percent, which of the three plans will produce the highest EPS?
  

• The Plan Current and E

• The plans Current and D

• Plan E

• Plan D

If two events are independent how do we calculate the and probability, P(E and F), of the two events?

(As a side note: this "and" probability, P(E and F), is called the joint probability of Events E and F. Likewise, the probability of an individual event, like P(E), is called the marginal probability of Event E.)

The probability that one has been to Antarctica given that one is a traveler is .05. The probability that one has not been to Antarctica given that one is not a traveler is .999. The probability that one is a traveler is .10.

a/ What is the probability of having been to Antarctica?

b/ What is the probability of not being a traveler, given that you have been to Antarctica?

The probability that a patient with a heart attack dies of the attack is 4%. Suppose we have 4 patients who suffer a heart attack

a) what is the probability that 2 will survive?

b) what is the probability that all will die?

c) what is the probability that less than 3 will survive?

d) what is the probability that all will survive?

Japanese auto companies manufacture cars in the United States for each of the following reasons EXCEPT ________.

Question 45 options:

There is single object to be sold to one of the n potential buyers. Each buyer has a valuation of vi for the object. Consider the auction rule where the winner is the highest bidder, and pays the minimum of all the bids, i.e. min{bi : i ∈ N}. In this game, truthtelling is a dominant strategy equilibrium. Is it true or false ?

1. For which system is ∆S<0?

2. Which pure substance under standard conditions would have the highest entropy?