what is the probability that the selected joint was judged to be defective by inspector a
Problem 13
A mutual fund company offers its customers several unlike funds: a money-market fund, iii different bond funds (curt, intermediate, and long-term), 2 stock funds (moderate and highrisk), and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the dissimilar funds are as follows:
$\brainstorm{array}{llll}\text { Money-market } & 20 \% & \text { High-gamble stock } & eighteen \% \\ \text { Short bond } & 15 \% & \text { Moderate-risk stock } & 25 \% \\ \text { Intermediate bail } & 10 \% & \text { Balanced } & 7 \% \\ \text { Long bond } & 5 \% & & \end{array}$
A client who owns shares in just one fund is randomly selected.
a. What is the probability that the selected individual owns shares in the balanced fund?
b. What is the probability that the individual owns shares in a bond fund?
c. What is the probability that the selected private does non own shares in a stock fund?
Problem fourteen
Consider randomly selecting a student at a certain university, and permit $A$ denote the event that the selected individual has a Visa credit menu and $B$ be the analogous event for a MasterCard. Suppose that $P(A)=.5, P(B)=.four$, and $P(A \cap B)=.25$.
a. Compute the probability that the selected individual has at to the lowest degree one of the two types of cards (i.e., the probability of the upshot $A \cup B$ ).
b. What is the probability that the selected individual has neither type of card?
c. Describe, in terms of $A$ and $B$, the event that the selected pupil has a Visa card but non a MasterCard, and then calculate the probability of this event.
Matt B.
Numerade Educator
Problem 15
A consulting firm presently has bids out on three projects. Let $A_{i}=\{$ awarded project $i\}$, for $i=$ $1,2,3$, and suppose that $P\left(A_{1}\right)=.22, P\left(A_{two}\right)=.25$, $P\left(A_{iii}\correct)=.28, P\left(A_{one} \cap A_{ii}\correct)=.eleven, P\left(A_{1} \cap A_{3}\right)=.05$, $P\left(A_{2} \cap A_{3}\right)=.07, P\left(A_{ane} \cap A_{2} \cap A_{3}\right)=.01$. Express in words each of the post-obit events, and compute the probability of each event:
a. $A_{one} \cup A_{ii}$
b. $A_{1}{ }^{\prime number} \cap A_{ii}{ }^{\prime number} \quad\left[\right.$ Hint : $\left.\left(A_{1} \cup A_{2}\right)^{\prime number}=A_{1}{ }^{\prime} \cap A_{2}{ }^{\prime}\right]$
c. $A_{1} \cup A_{2} \cup A_{3}$
d. $A_{1}{ }^{\prime} \cap A_{2}{ }^{\prime} \cap A_{3}{ }^{\prime}$
due east. $A_{1}{ }^{\prime} \cap A_{2}{ }^{\prime} \cap A_{3}$
f. $\left(A_{ane}^{\prime} \cap A_{two}^{\prime number}\right) \cup A_{3}$
Problem sixteen
A particular state has elected both a govemor and a senator. Let $A$ be the event that a randomly
selected voter has a favorable view of a certain party's senatorial candidate, and let $B$ be the respective result for that party's gubernatorial candidate. Suppose that $P\left(A^{\prime}\right)=.44, P\left(B^{\prime}\right)=$ $.57$, and $P(A \loving cup B)=.68$ (these figures are suggested by the 2010 general election in California).
a. What is the probability that a randomly selected voter has a favorable view of both candidates?
b. What is the probability that a randomly selected voter has a favorable view of exactly i of these candidates?
c. What is the probability that a randomly selected voter has an unfavorable view of at least i of these candidates.
Trouble 17
Consider the type of clothes dryer (gas or electric) purchased by each of five different customers at a certain store.
a. If the probability that at almost one of these customers purchases an electric dryer is . 428, what is the probability that at least 2 purchase an electric dryer?
b. If $P$ (all five purchase gas) $=.116$ and $P$ (all five purchase electrical) $=.005$, what is the probability that at to the lowest degree 1 of each blazon is purchased?
Harsh G.
Numerade Educator
Problem xviii
An individual is presented with three different glasses of cola, labeled $C, D$, and $P .$ He is asked to taste all three then list them in order of preference. Suppose the same cola has actually been put into all three glasses.
a. What are the elementary events in this ranking experiment, and what probability would you assign to each one?
b. What is the probability that $C$ is ranked first?
c. What is the probability that $C$ is ranked first and $D$ is ranked concluding?
Matt B.
Numerade Educator
Problem 19
Permit $A$ denote the consequence that the next request for assistance from a statistical software consultant relates to the SPSS package, and allow $B$ exist the event that the next request is for aid with SAS. Suppose that $P(A)=.30$ and $P(B)=.50$.
a. Why is it not the case that $P(A)+P(B)=1$ ?
b. Calculate $P\left(A^{\prime number}\right)$.
c. Calculate $P(A \cup B)$.
d. Calculate $P\left(A^{\prime number} \cap B^{\prime number}\correct)$.
Robin C.
Numerade Educator
Trouble 20
A box contains four $40-W$ bulbs, five $lx-W$ bulbs, and six $75-\mathrm{W}$ bulbs. If bulbs are selected one by one in random club, what is the probability that at least two bulbs must be selected to obtain one that is rated 75 Due west?
Matt B.
Numerade Educator
Problem 21
Man visual inspection of solder joints on printed excursion boards can be very subjective. Part of the problem stems from the numerous types of solder defects (due east.chiliad., pad nonwetting, knee visibility, voids) and even the caste to which a joint possesses 1 or more of these defects. Consequently, even highly trained inspectors can disagree on the disposition of a particular joint. In one batch of 10,000 joints, inspector A found 724 that were judged defective, inspector B plant 751 such joints, and 1159 of the joints were judged defective past at least one of the inspectors. Suppose that one of the 10,000 joints is randomly selected.
a. What is the probability that the selected joint was judged to be defective by neither of the two inspectors?
b. What is the probability that the selected joint was judged to exist lacking by inspector B but not by inspector $\mathrm{A}$ ?
Patrick Thou.
Numerade Educator
Problem 22
A factory operates 3 unlike shifts. Over the terminal year, 200 accidents have occurred at the factory. Some of these can exist attributed at least in part to dangerous working conditions, whereas the others are unrelated to working conditions. The accompanying table gives the percentage of accidents falling in each blazon of blow-shift category.
Suppose one of the 200 blow reports is randomly selected from a file of reports, and the shift and type of accident are adamant.
a. What are the simple events?
b. What is the probability that the selected accident was attributed to dangerous conditions?
c. What is the probability that the selected accident did not occur on the 24-hour interval shift?
Trouble 23
An insurance company offers 4 different deductible levels-none, low, medium, and high-for its homeowner's policyholders and iii different levels-depression, medium, and high-for its automobile policyholders. The accompanying tabular array gives proportions for the various categories of policyholders who have both types of insurance. For instance, the proportion of individuals with both depression homeowner's deductible and low auto deductible is $.06$ (six\% of all such individuals).
Suppose an individual having both types of policies is randomly selected.
a. What is the probability that the individual has a medium auto deductible and a loftier homeowner's deductible?
b. What is the probability that the private has a low auto deductible? A low homeowner'southward deductible?
c. What is the probability that the private is in the same category for both motorcar and homeowner'southward deductibles?
d. Based on your answer in part (c), what is the probability that the two categories are different?
e. What is the probability that the individual has at least one low deductible level?
f. Using the answer in role (east), what is the probability that neither deductible level is depression?
James S.
Numerade Educator
Trouble 24
The route used past a driver in commuting to piece of work contains two intersections with traffic signals. The probability that he must terminate at the commencement signal is $-iv$, the analogous probability for the 2d signal is .v, and the probability that he must stop at ane or more of the ii signals is .6. What is the probability that he must stop
a. At both signals?
b. At the showtime signal but not at the 2nd one?
c. At exactly i signal?
Matt B.
Numerade Educator
Problem 25
The computers of half-dozen faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other iv have chosen desktop machines. Suppose that merely 2 of the setups can be washed on a particular day, and the two computers to be set upwards are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered $i,two, \ldots, 6$, and then one outcome consists of computers ane and 2, another consists of computers 1 and 3 , and so on).
a. What is the probability that both selected setups are for laptop computers?
b. What is the probability that both selected setups are desktop machines?
c. What is the probability that at to the lowest degree one selected setup is for a desktop calculator?
d. What is the probability that at least i estimator of each type is chosen for setup?
Robin C.
Numerade Educator
Problem 26
Use the axioms to show that if one event $A$ is independent in another consequence $B$ (i.due east., $A$ is a subset of $B$ ), then $P(A) \leq P(B)$. [Hint: For such $A$ and $B, A$ and $B \cap A^{\prime}$ are disjoint and $B=A \cup\left(B \cap A^{\prime}\right)$, as can be seen from a Venn diagram.] For general $A$ and $B$, what does this imply virtually the relationship among $P(A \cap B), P(A)$, and $P(A \cup B)$ ?
Problem 27
The three major options on a car model are an automatic transmission $(A)$, a sunroof $(B)$, and an upgraded stereo $(C)$. If $70 \%$ of all purchasers asking $A, 80 \%$ asking $B, 75 \%$ asking $C, 85 \%$ request $A$ or $B, 90 \%$ request $A$ or $C, 95 \%$ request $B$ or $C$, and $98 \%$ request $A$ or $B$ or $C$, compute the probabilities of the following events. [Hint: "A or $B^{\prime \prime}$ is the event that at to the lowest degree one of the two options is requested; attempt drawing a Venn diagram and labeling all regions.]
a. The side by side purchaser will request at to the lowest degree 1 of the three options.
b. The side by side purchaser volition select none of the three options.
c. The side by side purchaser will request only an automated manual and neither of the other two options.
d. The next purchaser will select exactly one of these 3 options.
Trouble 28
A certain system can experience three different types of defects. Permit $A_{i}(i=1,2,three)$ denote the event that the system has a defect of type $i$. Suppose that
$$
\begin{aligned}
&P\left(A_{1}\correct)=.12 \quad P\left(A_{2}\right)=.07 \quad P\left(A_{3}\right)=.05 \\
&P\left(A_{1} \cup A_{2}\right)=.13 \quad P\left(A_{1} \loving cup A_{three}\correct)=.14 \\
&P\left(A_{2} \cup A_{3}\right)=.x \quad P\left(A_{1} \cap A_{2} \cap A_{three}\right)=.01
\stop{aligned}
$$
a. What is the probability that the organisation does non accept a type 1 defect?
b. What is the probability that the system has both type 1 and type 2 defects?
c. What is the probability that the system has both type one and type ii defects merely not a blazon iii defect?
d. What is the probability that the system has at most two of these defects?
Matt B.
Numerade Educator
Problem 29
In Do 7, suppose that any incoming private is as probable to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that
a. All 3 family members are assigned to the aforementioned station?
b. At most ii family members are assigned to the same station?
c. Every family member is assigned to a different station?
Robin C.
Numerade Educator
Trouble 30
Apply the proffer involving the probability of $A \loving cup B$ to the union of the two events $(A \cup B)$ and $C$ in society to verify the event for $P(A \cup B \cup C)$.
Matt B.
Numerade Educator
Source: https://www.numerade.com/books/chapter/probability-101/?section=65127
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