Section ATrue/False
Indicate whether the sentence or statement is true or false.

__F__1.Two events that are independent cannot be mutually exclusive.

__F__2.A joint probability can have a value greater than 1.

__F__3.The intersection of A and Ac is the entire sample space.

__T__4.If 50 of 250 people contacted make a donation to the city symphony, then the relative frequency method assigns a probability of .2 to the outcome of making a donation.

__T__5.An automobile dealership is waiting to take delivery of nine new cars. Today, anywhere from zero to all nine cars might be delivered. It is appropriate to use the classical method to assign a probability of 1/10 to each of the possible numbers that could be delivered.

__T__6.When assigning subjective probabilities, use experience, intuition, and any available data.

__F__7.P (AxB) d P (A)

__F__8.If P (A|B) = .4 and P (B) = .6, then P (AxB) = .667.

__T__9.Bayes' theorem provides a way to transform prior probabilities into posterior probabilities.

__T__10.If P (AyB) = P (A) + P (B), then A and B are mutually exclusive.

Section BMultiple Choice
Identify the letter of the choice that best completes the statement or answers the question.

__C__11.Which of the following is not a valid representation of a probability? a.35%
b.0
c.1.04
d.3/8

__A__12.A list of all possible outcomes of an experiment is called a.the sample space.
b.the sample point.
c.the experimental outcome.
d.the likelihood set.

__B__13.Which of the following is not a proper sample space when all undergraduates at a university are considered? a.S = {in-state, out-of-state}
b.S = {freshmen, sophomores}
c.S = {age under 21, age 21 or over}
d.S = {a major within business, no business major}

__B__14.In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the...

...chapter, you will be able to ONEDefine probability. TWO Describe the classical, empirical, and subjective approaches to probability. THREEUnderstand the terms experiment, event, outcome, permutation, and combination. FOURDefine the terms conditional probability and joint probability. FIVE Calculate probabilities applying the rules of addition and multiplication. SIXUse a tree diagram to organize and computeprobabilities. SEVEN Calculate a probability using Bayes theorem. What is probability There is really no answer to this question. Some people think of it as limiting frequency. That is, to say that the probability of getting heads when a coin is tossed means that, if the coin is tossed many times, it is likely to come down heads about half the time. But if you toss a coin 1000 times, you are not likely to get exactly 500 heads. You wouldnt be surprised to get only 495. But what about 450, or 100 Some people would say that you can work out probability by physical arguments, like the one we used for a fair coin. But this argument doesnt work in all cases, and it doesnt explain what probability means. Some people say it is subjective. You say that the probability of heads in a coin toss is 12 because you have no reason for thinking either heads or tails more likely you might change your view if you knew...

...assets are intended for consumption of sale realised during a year
Current assets is used for trading or transactions
Current assest have direct results of the profit gained in the business such as bank balance
Non-current assets are used for a longer duration (12 months)
Non-current assets used for productive investment purposes
Has very low impact of the profit gained as it only deals with things like machinery
6. the accumulated profit is also known as the retained earnings, retained profit and unappropriated profit. what is the accumulated profit and why do accountants and bookkeepers use different names for the same thing? (6 marks)
Accumulated profits is profits that are not paid as dividend but is transfered over to the accounts for the next year. Also can be used to reinvest in the core of the business to help pay off debts or to purchase a capital asset.
The reasons why accountants and bookkeepers use different names for the same thing is because bookkeepers are the people who record the financial transactions in a business in the form, of journals otherwise known as books, these transactions include receipts, slaes and payments made by the organisation. Bookkeepers are not certified accountants so they will use the term retained profits as this can easily mean profits you have retained over a period of time whereas an accountant is someone who keeps, audit and financial records of a individual or a business and prepares financial and...

...random variable is
A) generated by a random number table.
B) the variable for which an algebraic equation is solved.
C) a numerical measure of a probability experiment.. Ans = C
D) a qualitative attribute of a population.
4) Given the table of probabilities for the random variable x, does this form a probability distribution? Answer yes or no.
x 5 10 15 25
P(x) 0.1 –0.1 0.3 0.8 Ans = No
5) True or False: The expected value of a discrete random variable may be negative Ans = True
6) The table of probabilities of the random variable x is given as:
x 0 1 2 5
P(x) 0.5 0.2 0.2 0.1
Find the mean, µ and standard deviation, σ of x. Round answers to one decimal place. Ans = µ = 1.1, σ = 1.5
7) If p is the probability of success of a binomial experiment then the probability of failure is
A) 1 B) –p C) 1–p D) p + 0.5 Ans = C
8) A binomial experiment has 6 trials with the probability of success on any trial = p = 0.5. Find the probability of exactly 2 successes in the 6 trials. (Use the binomial probability distribution function.) Ans = 0.2344
9) Assume that male and female births are equally likely and the birth of any child does not affect the probability of the gender of any other children. Find the...

...Notation for the Binomial Distribution
P(S) The symbol for the probability of success
P(F) The symbol for the probability of failure
p The numerical probability of a success
q The numerical probability of a failure
P(S) = p and P(F) = 1 - p = q
n The number of trials
X The number of successes
The probability of a success in a binomial experiment can be computed with the following formula.
Binomial Probability Formula
In a binomial experiment, the probability of exactly X successes in n trials is
An explanation of why the formula works will be given in the following example.
Example 1:
A coin is tossed three times. Find the probability of getting exactly two heads.
Solution:
This problem can be solved by looking that the sample space. There are three ways to get two heads.
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
The answer is or 0.375.
The probability of a success in a binomial experiment can be computed with the following formula.
Binomial Probability Formula
In a binomial experiment, the probability of exactly X successes in n trials is
An explanation of why the formula works will be given in the following example.
Example 1:
A coin is tossed three...

...Hey guys, this is the probability Assignment. Last date for submission is 10 aug...
Q1. What is the probability of picking a card that was either red or black?
Q2. A problem in statistics is given to 5 students A, B, C, D, E. Their chances of solving it are ½,1/3,1/4,1/5,1/6. What is the probability that the problem will be solved?
Q3. A person is known to hit the target in 3 out of 4 shots whereas another person is known to hit the target in 2 out of 3 shots. Find the probability that the target being hit at all when they both try?
Q4. An investment consultant predicts that the odds against price of a certain stock will go up during the next week are 2:1 and the odds in the favor of the price remaining the same are 1:3.What is the probability that the price of the stock will go down during eth next week?
Q5. A bag contains 10 White and 6 Black balls. 4 balls are successfully drawn out and not replaced. What is the probability that they are alternately of different colors?
Q6.In a multiple-choice question there are 4 alternative answers, of which one or more are correct. A candidate will get marks in the question only if he ticks all the correct answers. The candidate decides to tick answers at random. If he is allowed up to 3 chances to answer the question, find the probability that he will get marks in the question?
Q7. A and B are two independent...

...I. ProbabilityTheory
* A branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.
* The word probability has several meanings in ordinary conversation. Two of these are particularly important for the development and applications of the mathematical theory of probability. One is the interpretation of probabilities as relative frequencies, for which simple games involving coins, cards, dice, and roulette wheels provide examples.
* It is the likeliness of an event happening based on all the possible outcomes. The ratio for the probability of an event 'P' occurring is P (event) = number of favorable outcomes divided by number of possible outcomes.
Example:
A coin is tossed on a standard 8×8 chessboard.
What is the theoretical probability that the coin lands on a black square?
Choices:
A. 0.5
B. 0.25
C. 0.42
D. 0.6
Correct answer: A
Solution:
Step 1: Theoretical probability = number of favorable outcomes / number of possible outcomes.
Step 2: The probability of the coin lands on the black square is 32.
Step 3: Total number of outcomes = 64.
Step 4: P (event) =
Step 5: == 0.5
Step 6: The theoretical...

...until you have a signed contract clearly stating and agreeing to payment terms.
2. Once you begin doing business with someone, make sure you stamp your invoices with the date that payment is due to you. Don't rely on the customer to look at the invoice date and add 30 days -- or whatever your payment terms are -- to determine the pay date.
3. Offer discounts for early payment and add interest to late payments. A typical discount is two percent to three percent off the total if the bill is paid within 10 days of the invoice date. The maximum amount of interest that can be charged varies by state.
4. Phone customers and start trying to collect the day after a payment is due.Never wait -- let them know that you keep close track of your accounts receivable.
5. Until a customer pays their bills, don't do any more business with them. Do not bend on this rule – you'll only cause yourself more problems and scuttle any chance of collecting what you're owed. If you really want to keep doing business with a customer who owes you, insist that any new products or services they receive from you are COD -- cash on delivery.
Checklist: What If You Can't Collect on Payments Due?
By AllBusiness.com
Here are some effective ways to get paid by delinquent customers:
-- Maintain an accurate accounts receivable aging report.
-- Call as soon as a customer is late with a payment.
-- Don´t give your delinquent customers an...

...ProbabilityTheory and Game of Chance
Jingjing Xu
April 24, 2012
I. INTRODUCTION
Probabilitytheory is the mathematical foundation of statistics, and it can be applied to many areas requiring large data analysis. Curiously, that the study on probabilitytheory has its root in parlor games and gambling. In 17th century, dice gambling was a very common entertainment among the upper class. An Italian mathematician and gambler Gerolamo Cardano founded the concept of probability by studying the rules of rolling dice: since a die is a cube with each of its six faces showing a different number from 1 to 6, when it is rolled, the probability of seeing each number is equal. Therefore, some of the gamblers began to wonder, that taking a pair of dice and rolling them a couple of times, which has the larger probability of seeing a sum of 9 or seeing a sum of 10? What about seeing double sixes? In a correspondence between Blaise Pascal and Pierre Fermat, the problems were resolved, and this triggered the first theorem in the modern theory of probability.
II. BASIC DEFINITIONS
Definition 1
In probabilitytheory, the sample space,...

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