A constructor has two subcontractors for his excavation Experience shows that in 60% of the time, subcontractor A was available to do a job, whereas subcontractor B was available 80% of the time. Also, the contractor is able to get at least one of these two subcontractors 90% of the time. Suppose EA denotes the event that subcontractor A is available, and EB denotes thatsubcontractor B is Are EA and EB statistically independent? Explain. Are EA and EB mutually exhaustive? Explain. Are EA and EB collectively exhaustive? Explain

A constructor has two subcontractors for his excavation Experience shows that in 60% of the time, subcontractor A was available to do a job, whereas subcontractor B was available 80% of the time. Also, the contractor is able to get at least one of these two subcontractors 90% of the time. Suppose EA denotes the event that subcontractor A is available, and EB denotes thatsubcontractor B is Are EA and EB statistically independent? Explain. Are EA and EB mutually exhaustive? Explain. Are EA and EB collectively exhaustive? Explain

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

Similar questions

An anger-management course claims that, after completing its seminar, participants will lose their tempers less often. Always a skeptic, you decide to test this claim. A random sample of 12 seminar participants is chosen, and these participants are asked to record the number of times that they lost their tempers in the two weeks prior to the course. After the course is over, the same participants are asked to record the number of times that they lost their tempers in the next two weeks. The following table lists the results of the survey. Using these data, test the claim at the 0.01 level of significance assuming that the population distribution of the paired differences is approximately normal. Let participants before completing the anger-management course be Population 1 and let participants after completing the anger-management course be Population 2. Number of Times Temper Was Lost during a Two-Week Period Before 10 6 8 10 6 3 10 3 8 After 6 7 4 4 8 6 4 9 3 7 Copy Data Step 2 of 3:…
It has been observed that some persons who suffer colitis, again suffer colitis within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode? Select the [Alternative Hypothesis,…
An anger-management course claims that, after completing its seminar, participants will lose their tempers less often. Always a skeptic, you decide to test this claim. A random sample of 12 seminar participants is chosen, and these participants are asked to record the number of times that they lost their tempers in the two weeks prior to the course. After the course is over, the same participants are asked to record the number of times that they lost their tempers in the next two weeks. The following table lists the results of the survey. Using these data, test the claim at the 0.01 level of significance assuming that the population distribution of the paired differences is approximately normal. Let participants before completing the anger-management course be Population 1 and let participants after completing the anger-management course be Population 2. Number of Times Temper Was Lost during a Two-Week Period Before 6 7 10 11 8 12 9 8 3 7 11 12 After 5 5 11 8 8 8 6 9 4 6 9 12…
3. An unloaded, 4-sided dice is rolled twice. Let X be the maximum number obtained from the two rolls, and Y be the minimum number from the two rolls. (The dice can show the numbers 1, 2, 3, or 4, each with probability 1/4. As an example, if the two rolls are 1 followed by 3, then X = 3 and Y = 1.) (a) Find the joint pmf of X and Y. (b) Find the conditional pmf of X given that Y = 2. (Hint: part (a) is similar to a problem from Modelling Uncertainty. Please express your answers in table form, and please use fractions in lowest terms.)
A company manufacturing CDs is working on a new technology. A random sample of 646 Internet users were asked: "As you may know, some CDs are being manufactured so that you can only make one copy of the CD after you purchase it. Would you buy a CD with this technology, or would you refuse to buy it even if it was one you would normally buy?" Of these users, 59% responded that they would buy the CD. Complete parts a and b below. a) Create a 99% confidence interval for this percentage. ( 54.008 %, 63.993 %) (Round to three decimal places as needed. Use ascending order.) b) If the company wants to cut the margin of error by two thirds, how many users must they survey? The company must survey a total of (Type a whole number.) users
It has been observed that some persons who suffer renal failure, again suffer renal failure within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 75 people in the second group and this group will be administered a placebo. After one year, 10% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.01, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode? Select the [Alternative…
Suppose that we want to estimate the true rate r of covid-positive people in a popu- lation (where they are reluctant to disclose their status). We use the two-coin-toss method, and those who toss two heads will lie about their status, reporting the opposite status. After flipping their coins, 36% of the people report that they are covid-positive. What is our estimate for the rate r of covid-positive people in this population?
At a tourist place, it has been observed that: 40% of the women like to travel with a Purse, 30% of the women like to travel with a Sunglass, 35% of the women like to travel with a Watch, and it is also noted that: 12% of the women like to travel with a Purse and a Sunglass, 3% of the women like to travel with all these three luxuries, 10% of the women like to travel with a Purse and a Watch, and 8% of the women like to travel only with a Sunglass. Purse Watch Sunglass Modern women like luxury. A woman What percentages of the women like to travel with Watch only? a. 30% b. 27% ♥ What percentages of the women do not like to carry them C. 40% (Purse, Sunglass, Watch)? v What percentages of women like to travel with Purse only? v What percentages of women like to travel with both Watch f. 13% and Sunglass? d. 65% e. 15% g. 52% v What percentages of women like to travel either with Watch or with Sunglass? v What percentages of women like to travel with Sunglass only? h. 8% i. 21%
A researcher wants to determine whether adolescents spend more time in a day around friends than adults do. He gathers a sample of n =10 adolescents (aged 12-17) and a sample of n =6 adults (aged 25-32). The researcher finds that the average time spent around friends for adolescents is M1= 3 hours with a SS1 of 44. He also finds that the average time spent around friends for adults is M2= 2 hours with a SS2 of 40. a. Do you use a one- or two-tailed test? What is the critical/cut-off t value with an alpha level of α = .01? b. What is the variance? c. What is the estimated standard error? d. What is the value of the t statistic? e. Do we reject or fail to reject the null hypothesis (α = .01)? Why? f. Calculate and report the variance explained ( r2)
An education researcher claims that at most 7% of working college students are employed as teachers a= 0.01, is there enough evidence to reject the researcher's claim? Complete parts (a) through (e) below. r teaching assistants. In a random sample of 500 working college students, 9% are employed as teachers or teaching assistants. At (a) Identify the claim and state H, and H Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. At most 7 % of working college students are employed as teachers or teaching assistants. O B. % of working college students are employed as teachers or teaching assistants. O C. The percentage of working college students who are employed as teachers or teaching assistants is not %. O D. More than % of working college students are employed as teachers or teaching assistants. Let p be the population proportion of successes, where a success is a…
Suppose there is a 3-stage experiment that are pairwise independent (i.e. they’re all independent from eachother). If stage one has 5 outcomes stage two has 6 outcomes and stage three has 2 possible outcomes, howmany outcomes does the experiment itself have?
Overbooking is the practice of selling more items than are currently available. Overbooking is common in the travel industry; it allows a vehicle (airline, train, bus, cruise ship, hotel, and so forth) to operate at or near capacity, despite cancellations, no-shows, or late arrivals. Overselling is when more confirmed customers show up to use the vehicle than there is space available. When this happens, at least one customer will be denied the service that they paid for, either voluntarily (sometimes with an incentive provided by the supplier) or involuntarily. This is called getting "bumped." Suppose that for a particular flight, an airline believes that 2% of ticket holders do not make the flight. The jet making the trip holds 189 passengers. If the airline sells 192 tickets, what is the probability that the flight will be oversold and they will have to bump a passenger? Assume that cancellations are independent. Calculate the probabilities that one, two, and three people will be…