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ISU / Business / BUS 205 / in a survey, respondents were asked to indicate their favorite brand o

in a survey, respondents were asked to indicate their favorite brand o

in a survey, respondents were asked to indicate their favorite brand o

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Bus 205 2/13/17 Chapter 4 notes ∙ Probability- the chance that a particular event will occur ∙ Experiment- a process that produces a single outcome whose result cannot  be predicted with certainty ∙ Sample space- the collection of all outcomes that can result from a selection,  decision, or experiment ∙ Event- a collection of experimental outcomes ∙ Mutually exclusive events- two events are mutually exclusive if the  occurrence of one event precludes the occurrence of the other event. ∙ Independent events- two events are independent if the occurrence of one  event in no way influences the probability of the occurrence of the other  event ∙ Dependent events- two events are dependent if the occurrence of one event  impacts the probability of the other event occurring ∙ Classical probability assessment- the method of determining probability  based on the ratio of the number of ways of an outcome or event of interest  can occur to the number of ways any outcome or event can occur when the  individual outcomes are equally likely ∙ Relative Frequency Assessment- the method that defines probability as the  number of times an event occurs divided by the total number of times an  experiment is performed in a large number of trials. ∙ Subjective Probability assessment- the method that defines probability of an  event as reflecting a decision maker’s state of mind regarding the chances  that the particular event will occur. Chapter 4 Homework ∙ Question 1 o In a survey, respondents were asked to indicate their favorite brand of cereal. They were  only allowed one choice. What is the concept that implies it is not possible for a single  respondent to state more than one brand as their favorite cereal?  Mutually exclusive events ∙ Question 2 o If two people are asked to list their choices of favorite pizza topping  from among bacon (b), onions (o), and pepperoni (p), list the sample  space showing the possible outcomes.   (b,b), (b,o), (b,p), (o,b), (o,o), (o,p), (p,b), (p,o), (p,p) ∙ Question 3 o A bicycle company makes two mountain bike models that each come in three colors. Use the following table, which shows the production  volumes for one week, to answer parts a through c. Color Model Blue Brown White


What is the concept that implies it is not possible for a single respondent to state more than one brand as their favorite cereal?



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Ro-50 287 85 210 Hd-99 37 217 125

∙ Based on the relative frequency assessment method, what is  the probability that manufactured item is blue? o P(blue)=.3371 ∙ What is the probability that the product manufactured is an  ro-50 o P(ro-50)=.6056 ∙ What is the probability that a product manufactured is a ro 50 and blue? o P(ro-50 and blue)=.2986 1. Question 4 a. A successful barbecue chain sells its beef, pork, and chicken items to  three kinds of customers: dine-in, delivery, and pickup. Last year’s  sales showed that 12,762 orders were dine-in (d), 5,895 were delivery  orders €, and 3,133 orders were pickup (p). Suppose an audit of last  year’s sales is being conducted. Complete parts a through c. i. If a customer order is selected at random, what is the probability it will be a pickup order? 1. P(pickup)=.1438 ii. What method of probability assessment is used to determine the probability in part a? 1. Relative frequency assessment iii. If two customer orders are selected at random, list the sample  space indicating the type of order for both customers 1. (d, d), (d, e), (d, p), (e, d), (e, e), (e, p), (p, d), (p, e), (p, p) 2. Question 5 a. A company produces scooters used by small businesses that find them convenient for  making short deliveries. The company is notified whenever a scooter breaks down, and  the problem is classified as being either mechanical or electrical. The company then  matches the scooter to the plant where it was assembled. The data table to the right  contains a random sample of 200 breakdowns. Use the data file and the relative  frequency assessment method to complete parts a through c. 

Electrical Mechanical Total Plant 1 21 46 67 Plant 2 75 58 133 Total 96 104 200


∙ Based on the relative frequency assessment method, what is the probability that manufactured item is blue?



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1. What is the probability a scooter was assembled at plant 2? a. P(plant 2).665 2. What is the probability that a scooter breakdown was due to a  mechanical problem? a. P(mechanical)= .52 3. What is the probability that a scooter breakdown was due to an  electrical problem and the scooter was assembled at plant 1?a. P(electrical and plant 1)=.105 1. Question 6 a. Three events occur with probabilities p (e1) =.38, p (e2) =.17, and p  (e3) =.46. If the event B occurs, the probability becomes P (e1b) = .23, P (b) =.28. Complete parts a through c. i. Calculate P (E1 and B) 1. Use technology or the formula for the Multiplication Rule  shown below, where A1 and A2 are and two events, to  find the probability of the event. a. P(A1 and A2) = P (A1) P (A2|A1) 2. What is P (B) a. = .28 3. What is P (E1B) a. =.23 4. Substitute P (B)=.28 and P (E1|B)=.23 into the formula  from the previous step to calculate P (E1 and B) a. P (E1 and B) = P (B)P (E1|B) i. =.28*.23 1. =.0644 ii. Use technology or the formula for the addition rule shown below, where A1 and A2 are any events, to find the probability of the  event.  1. P (A1 or A2)= P (A1) + P(A2) – P (A1 and A2) a. P (E1 or B)= P (E1) + P (B) – P ( E1 and B) i. =.38 +.28 -0.0644 1. =.5956 iii. Use technology or the formula for the multiplication rule for  independent events shown below, where A1 and A2 are any tow  events, to find the probability of the event. 1. P (A1 and A2) =P (A1) P(A2) 2. P (E1 and E2 and E3) = P (E1) P(E2) P(E3) a. =.38*.17*.46 i. .0297 2. Question 7 a. The table to the right gives a breakdown of 2,167 civil cases that were appealed. The  outcome of theappeal, as well as the type of trial (judge or jury), was determined for each case. Suppose one of the cases is selected at random and the outcome of the appeal  and type of trial are observed. Complete parts a through c.

Jury Judge Totals Plaintiff trial win reversed 199 74 273 Plaintiff trial win affirmed/dismissed 442 250 692 Defendant trial  win-reversed 101 72 173 Defendant trial  win affirmed/dismissed 735 294 1029


If a customer order is selected at random, what is the probability it will be a pickup order?



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Totals 1477 690 2167

1. What is the probability that a randomly selected case is a judge  trial? a. The probability that a random selected case is a judge trial is i. .318 b. What is the probability that the final outcome of a randomly  selected case is “plaintiff trial win is reversed? i. .126 c. If a randomly selected case is a jury trial, what is the  probability that the final outcome of the case is a plaintiff  trial win?.
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