The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 38% of all purchasers request A, 45% request B, 66% request C, 56% request A or B, 75% request A or C, 71% request B or C, and 78% request A or B or C, determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.

The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 38% of all purchasers request A, 45% request B, 66% request C, 56% request A or B, 75% request A or C, 71% request B or C, and 78% request A or B or C, determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: In a manufacturing plant, three machines, A, B, and C, produce 41%, 38%, and 21%, respectively, of…

A: Given , P( A ) = 0.41 , P( defective | A ) = 0.01 P( B ) = 0.38 , P( defective | B ) = 0.02 P( C )…

Q: The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is…

A: Solution According to the guideline we solve only three subparts of one question

Q: A computer manufacturer uses chips from three sources. Chips from sources A, B, and C are defective…

A: There are three manufacturer of chips A,B and C and the proportions of chips from A,B and C are 0.5…

Q: The Battery company manufactures electric batteries. The probability that the finished battery is…

A: Given data, probability that the finished battery is defective is 0.05 probability that the packer…

Q: You are playing a video game where your character, Levi, is fighting an opponent. Levi has a 20%…

A: Since you have posted multiple sub-parts, we will solve the first three sub-parts for you. To get…

Q: Given two events G and H, the probabilities of each occurring are as follows: P(G) = 0.35; P(H) =…

A: First question: For an non null event A it known that P(A) + P(Ac) = 1.

Q: The Apollo module has five components: the main engine, the propulsion system, the command service…

A: Given Consider the following situation: The Apollo module has five components: the main engine, the…

Q: The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B),…

A: Given: PA=0.34PB=0.52PC=0.72PA ∪ B=0.59PA∪ C=0.78PB ∪ C=0.79PA ∪ B ∪ C=0.83

Q: The major airline industry is subject to labor strikes by the pilots, mechanics, and flight…

A: Event A defines strike by the pilots, event B defines the strike by the mechanics and event C…

Q: The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B),…

Q: most popular opti Lype of Tiew (A), equest A, 59% request B, 75% request C, 70% request A or B, 87%…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: A game show contestant is offered the option of receiving a computer system worth $2200 or accepting…

A: Given Data:Prize (x)P(x)49000.29000.15We have to find the expected winning if contestant were turn…

Q: 1. Calculate the correlation between the IQ of a person with the number of hours spent in the class…

A: Given information:- IQ Hours of class per Week 106 7 86 0 100 27 101 50 99 28 103 29…

Q: determine the probabilities of the following events. [Hint: "A or B" is the event that at least one…

Q: Under a proposed new federal law, poker in US casinos would henceforth be played with a 65 card deck…

A: Given information: Under a proposed new federal law, poker in US casinos would henceforth be played…

Q: The nursing department of a college surveyed two hundred graduates from their programs about their…

A: Given Data: P( bachelor's degree)=0.45 P( working in nursing)=0.85 P( in nursing and bachelors)=0.4

Q: Human blood types are typically classified by the ABO blood group and the Rh blood group systems.…

A: First let us create a frequency table of the blood types from the given Venn diagram. A B AB O…

Q: A dealership sent out fliers to prospective customers, indicating that they had already won one of…

A: Given the three prices are either a new car valued at $15,800, a $500 gas card, or a $5 gift card.…

Q: During half-time of a basketball game there is a half-court shot competition. Three fans are chosen…

A: The first fan has a probability of making shot =0.15 The second fan has a probability of making shot…

Q: An actuarial student studies for an exam using a review course, a textbook, or both. 70% of…

A: We have to use Bayes theorem to solve this problem.

Q: A manufacturing process at Bake first stage is 15 percent, and the probability of defective compone…

A: There are four possibilities: (i) P(Defective in stage 1 and defective in stage 2 (Completely…

Q: Based on data from a car bumper sticker study, when a car is randomly selected, the number of bumper…

A: Given Information: X 0 1 2 3 4 5 6 7 8 9 P(X) 0.806 0.081 0.038 0.024 0.014 0.013 0.009 0.007…

Q: Three airlines serve a small airport. Airline A has 55% of all scheduled flights, airline B has 33%…

Q: A manufacturing company is faced with the problems of choosing four products to manufacture. The…

A: Given Products Probabilities Good satisfactory poor A 0.60 0.20 0.20 B 0.75…

Q: In a game of chance, a spinner is divided into four regions: red, blue, green, and yellow. The…

A: we can use the formula for the expected value of a discrete random variable.The expected value…

Q: Components of a certain type are shipped to a supplier in batches of ten. Suppose that 48% of all…

A: Given information: P(B0) = 0.48 P(B1) = 0.32 P(B2) = 0.20

Q: A crucial pumping process in a power plant is safely designed in a more conservative approach so…

A: Probability is the chance of occurrence observation favorable to enter in the sample or event. Where…

Q: The Apollo module has five components: the main engine, the propulsion system, the command service…

A: Answer: From the given data, The Apollo module has five components, The main engine, the propulsion…

Q: 5.1.2Suppose that Z~ N(0, 1). (a) P(Z ≤ -0.77) (b) P(Z≥ 0.32) (c) P(-3.09 ≤ Z≤ -1.59)

A: given data standard normal distributionZ~N(0,1) as per guideline expert have to solve first 3…

Q: 35% of all college students major in STEM (Science, Technology, Engineering, and Math). If 31…

A: Step 1:To solve these problems, we can use the binomial probability formula, since each student…

Q: Alogional automobile dealership sent out fliers to prospective customers indicating that they had…

A: Given:

Q: The probability that both locations will have high sales next quarter is (E)

A: Here Given Automobile dealer owns two dealership at two different location And Probability of…

Q: If the total number of data sample is 100, how many suitable number of classes if the data samples…

A: Solution-: Given: N=100 We find how many suitable number of classes in the data set?

Q: Suppose Alice is deciding whether or not to go to a New York Giants game. Alice's enjoyment and thus…

A: p ( gaints lose and its snows ) is =?

Q: The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is…

A: (a) Obtain the probability value of P(A). The probability value of P(A) is obtained below as…

Q: In a certain assembly plant, three machines A1, A2, and A3 make 30%, 45% and 25% respectively, of…

A: Let, D=defective Given that: P(A1)=30%=0.30 P(A2)=45%=0.45 P(A3)=25%=0.25 P(D|A1)=3%=0.03…

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 38% of all purchasers request A, 45%
request B, 66% request C, 56% request A or B, 75% request A or C, 71% request B or C, and 78% request A or B or C, determine the probabilities of the following events.
[Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.]
(a) The next purchaser will request at least one of the three options.
(b) The next purchaser will select none of the three options.
(c) The next purchaser will request only an automatic transmission and not either of the other two options.
(d) The next purchaser will select exactly one of these three options.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Here are three lotteries played by three individuals that cost $100. Could you tell whether they are risk-neutral, risk-seeking(loving) or risk-averse? the percentages in () are the probabilities associated with the events. 1)Win (50%): gets $180, lose (50%): gets $40; 2)Win (50%): gets $160, lose (50%): $0; 3)Win (20%): gets $300, lose (80%): gets $50. which one of these individuals are more likely to pursue entrepreneurship? Briefly explain why.
The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (8), and an automatic transmission (C). If 46% of all purchasers request A, 57% request 8, 76% request C, 71% request A or 8, 89% request A or C, 88% request 8 or C, and 94% request A or 8 or C, determine the probabilities of the following events. [Hint: "A or 8" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. 0.85 X (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.
There are three modes of transporting material from Boston to Houston: by land (either by highway or railway), seaor air. Half of the materials are transported by land20% by sea, and the rest by air. Also, 60% of all land transportation is by highway and the rest is by rail shipments.Cargo traveling by each mode of transportation has a different probability of being damaged during shipment. The percentages of damaged cargo are as follows: 12% by highway, 3% by rail, 5% by seaand 2% by airIf a damaged cargo is received, what is the probability that it was shipped by sea?
In the current first-year class of a community college, all the students come from three local high schools. Schools I, II, and III supply respectively 30%, 40%, and 30% of the students. The failure rate of students is 4%, 3%, and 6%, respectively. Given that a student passes, what is the probability that he or she came from school I?
A regional automobile dealership sent out fliers to prospective customers indicating that they had already won one of three different prizes: an automobile valued at $30,000, a $125 gas card, or a $5 shopping card. To claim his or her prize, a prospective customer needed to present the flier at the dealership's showroom. The fine print on the back of the flier listed the probabilities of winning. The chance of winning the car was 1 out of 31,729, the chance of winning the gas card was 1 out of 31,729, and the chance of winning the shopping card was 31,727 out of 31,729. Complete parts (a) through (d). a. How many fliers do you think the automobile dealership sent out? Assume there is one car and one gas card available. 31729 fliers C b. Using your answer to (a) and the probabilities listed on the flier, what is the expected value of the prize won by a prospective customer receiving a flier? H=$5.95 (Round to the nearest cent as needed.) c. Using your answer to (a) and the probabilities…
At the Washington University 35%, 25% and 40% of the students in Calculus are taught by Prof. A, Prof. B and Prof. C, respectively. The respective probabilities of failing in Calculus for the three professors are 6%, 7% and 5%. A student in Calculus in the previous semester was randomly selected and was found out to have failed in the subject. Under which class most likely did he belong?
Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can’t recall the brand name and does not wish to return home to find the old can of paint. So, she selects two of the three brands of paint at random and buys them. What is the probability that she matched the paint brand? Her husband also goes to the paint store and fails to remember what brand to buy. So, he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband’s selections independent of the wife’s selections?)
The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 36% of all purchasers request A, 47% request B, 69% request C, 54% request A or B, 75% request A or C, 76% request B or C, and 78% request A or B or C, determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.
Samsung wants to run ads for its new Galaxy Phone. Based on a survey conducted, Samsung assigned probabilities to the following events: individual purchased a Galaxy Phone with a probability of 55%, individual recalls seeing the ad with a probability 70%, and individual did not purchase the Galaxy Phone nor recalls seeing the ad with a probability of 40%. What is the probability that the individual recalls seeing the ad or purchases the Galaxy Phone? a. 60% b. 30% c. None of these d. 65% e. 45%
In an inspection of automobiles in a certain Country, 60% of all automobiles had emissions that did not meet EPA regulations. For a random sample of 10 automobiles, compute the following probabilities: a. All 10 automobiles failed the inspection. b. Exactly 6 of the 10 failed the inspection. c. Six or more failed the inspection. d. All 10 passed the inspection.
The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 53% of all purchasers request A, 60% request B, 76% request C, 70% request A or B, 91% request A or C, 86% request B or C, and 93% request A or B or C, determine the probabilities of the following events. [Hint: "A or B" is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] (a) The next purchaser will request at least one of the three options. (b) The next purchaser will select none of the three options. (c) The next purchaser will request only an automatic transmission and not either of the other two options. (d) The next purchaser will select exactly one of these three options.
Alex, Natasha, and Juan fill orders in a fast-food restaurant. Alex incorrectly fills 20% of the orders he takes. Natasha incorrectly fills 12% of the orders she takes. Juan incorrectly fills 5% of the orders he takes. Alex fills 30% of all orders, Natasha fills 45% of all orders, and Juan fills 25% of all orders. An order has just been filled. A. If the order was filled by Juan, what is the probability that it was filled correctly? B. Who filled the order is unknown, but the order was filled incorrectly. What are the revised probabilities that Alex, Natasha, or Juan filled the order? C. Who filled the order is unknown, but the order was filled correctly. What are the revised probabilities that Alex, Natasha, or Juan filled the order?