##### Question

In: Statistics and Probability

# 1.)the chair of the board of directors says, "there is a 50% chance this company will...

1.)the chair of the board of directors says, "there is a 50% chance this company will earn a profit, a 30% chance it will lose money next quarter." a.) use an addition rule to find the probability the company will not lose money next quarter B.) use he complement rule to find the probability it will not lose money next quarter.

2.)suoose P(X1 )=.75 and P(Y2|X1)=.40. what is the joint probability of X1 & Y2

3.)An investor owns three common stocks. Each stock, independent of the others, has equally likely chances of (1) increasing in value. (2) decreasing in value, or (3) remaining same value. List the possible outcomes of this experiment. Estimate the probability at least two of the stocks increase in value.

## Solutions

##### Expert Solution

1.)the chair of the board of directors says, "there is a 50% chance this company will earn a profit, a 30% chance it will lose money next quarter." a.) use an addition rule to find the probability the company will not lose money next quarter B.) use he complement rule to find the probability it will not lose money next quarter.

a)

Pr(neither lose nor profit) = 1 - 0.50 - 0.30 = 0.20

Pr(company will not lose money next quarter) = Pr(Profit) + Pr(neither lose nor profit)

Pr(company will not lose money next quarter) = 0.50 + 0.20 = 0.70

b)

Using the complement rule,

Pr(company will not lose money next quarter) = 1 - Pr(company will lose money next quarter)

Pr(company will not lose money next quarter) = 1 - 0.30 = 0.70

2)

Using the conditional probability law,

3)

For each stock, there are three possible outcomes, such that (1) increasing in value. (2) decreasing in value, or (3) remaining the same value

Hence total possible outcomes for three stocks = 3*3*3 = 27

Let A represents increasing in value, B represents decreasing in value, and C represents remaining the same value.

 Outcome Stock 1 Stock 2 Stock 3 1 A A A 2 A A B 3 A A C 4 A B A 5 A B B 6 A B C 7 A C A 8 A C B 9 A C C 10 B A A 11 B A B 12 B A C 13 B B A 14 B B B 15 B B C 16 B C A 17 B C B 18 B C C 19 C A A 20 C A B 21 C A C 22 C B A 23 C B B 24 C B C 25 C C A 26 C C B 27 C C C

(count the number of outcomes where 'A' appears 2 or 3 times then divide it by total number of outcomes = 27)

## Related Solutions

##### 1. A firm's stock has 50% chance of a 13% rate of return and a  50% chance...
1. A firm's stock has 50% chance of a 13% rate of return and a  50% chance of a 20% rate of return. What is the standard deviation of return for this stock? Answer as a percent return  to the nearest hundredth of a percent as in xx.xx without entering a percent symbol.   2. A firm's stock has 50% chance of a 35% rate of return. a 30% chance of a 18% rate of return. and a 20% chance of a -24%...
##### a There is a 50% chance of thunderstorms on Monday, a 50% chance on Tuesday and...
a There is a 50% chance of thunderstorms on Monday, a 50% chance on Tuesday and a 50% chance on Wednesday. Assume these are independent events. What is the probability that there will be thunderstorms on Monday, Tuesday, and Wednesday? Show your work.   b) A student says that if P(A) = P(A|B), then A and B must be independent events. Is the student correct? Explain.  Give a real life example that can be represented by P(A) = P(A|B). c) Describe the...
##### There are 15 members on the board of directors for a Fortune 500 company. If they...
There are 15 members on the board of directors for a Fortune 500 company. If they must select a chairperson, a first vice chairperson, a second vice chairperson, and a secretary. (a) How many different ways the officers can be selected? Show work. (b) Please describe the method used and the reason why it is appropriate for answering the question. A researcher wants to conduct a clinical trial on a new medicine for a rare disease. She plans to randomly...
##### At a meeting of the board of directors of Barby Limited it was decided : 1....
At a meeting of the board of directors of Barby Limited it was decided : 1. To redeem the redeemable preference shares of the company on 30 September 2006. 2. To achieve this by a fresh issue of the maximum number of ordinary shares of permissible without the necessity of calling a meeting of shareholders. 3. That the issue price for the proposed issue would be R1, 20 per share 4. That the redemption should be made in such a...
##### Please describe the relationship of the Board of Directors for Company Bravo to the company. Provide...
Please describe the relationship of the Board of Directors for Company Bravo to the company. Provide the purpose, details of general responsibilities, etc. with support. What types of items would constitute a Board members breach of duty to the company? Name and explain with details and support. Is it acceptable for a company’s Board of Directors to approve a personal loan to the CEO of the company as long as the vote is unanimous? Why or Why not? Please explain...
##### Jac Flyhigh is Chair of the Board of Exeed Company. The company has been experiencing growth...
Jac Flyhigh is Chair of the Board of Exeed Company. The company has been experiencing growth placing a strain on finances and increasing levels of risk. Despite having put in place a budget that predicted a profit of $1m, expenditure has blown out over the year and the company is potentially going to record a loss of$360,000. In order to be able to report a profit to shareholders the Chief Financial Officer is proposing that the company recognise additional...
##### Karim is the president of Samirad Company. At a meeting of the board of directors, Karim...
Karim is the president of Samirad Company. At a meeting of the board of directors, Karim was asked to explain why audits of the company are made by (1) internal auditors (2) independent auditors, and (3) government auditors. One board member suggested that the company's total audit expense might be less if all auditing was done by internal auditors. Karim was unable to distinguish between the three types of auditors or to satisfactorily respond to the board member's suggestion. Instructions:...
##### 1. Assume there are 5 seats to vote in the board of directors. There are only...
1. Assume there are 5 seats to vote in the board of directors. There are only three shareholders: Arnold (100 shares), Beth (40 shares), and Charles (60 shares). With cumulative voting Charles can elect at least _________. Select one: a. zero directors b. one director c. two directors     d. three directors    2If a savings account pays an annual interest of 2% compounded quarterly, then the quarterly interest rate should be less than 0.5%. Select one: True False 3.If...
##### 1. There are 9 members on a board of directors. If they must form a subcommittee...
1. There are 9 members on a board of directors. If they must form a subcommittee of 6 members, how many different subcommittees are possible? 60,480 720 84 531,441 2. A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5? 16 3. A pitching machine throws 70% strikes and 30% balls. Five pitches will be thrown by the machine. What is the probability the machine...
##### On January 1, 2017, Company One’s Board of Directors approved granting 5,000 stock options to a...
On January 1, 2017, Company One’s Board of Directors approved granting 5,000 stock options to a select group of senior employees. The requisite service period is five years with 20% of the options vesting each year from 2017 to 2021. The fair value of the option is as below: Jan 1, 2017 $20 Dec 31, 2017$21 Dec 31, 2018 $22 Dec 31, 2019$23 Dec 31, 2020 $24 Dec 31, 2021$25 Based on the description in question, determine...