Conditional ProbabilityThe following table summarizes the analysis of samples of galvanized steel for coating weight andsurface roughness:SurfaceRoughnessHighLowCoating WeightHigh1288Low1634(a) If the coating weight of a sample is high, what is the probability that the surface roughness is high?(b) If the surface roughness of a sample is high, what is the probability that the coating weight is high?(c) If the surface roughness of a sample is low, what is the probability that the coating weight is low?Multiplication and Total Probability rulesThe probability is 1% that an electrical connector that is kept dry fails during the warranty periodof a portable computer. If the connector is ever wet, the probability of a failure during the warrantyperiod is 5%. If 90% of the connectors are kept dry and 10% are wet, what proportion ofconnectors fail during the warranty period?

Farmula used P(A|B)=P(A and B)/P(B) Note: According to Bartleby guidelines expert solve only one…

Answered: Conditional Probability The following…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

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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...

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28. Green Behavior: Purchasing Habits A recent Harris Poll on green behavior showed that 25% of adults often purchase used items instead of new ones. Consider a random sample of 75 adults. Let p be the sample proportion of adults who often purchase used instead of new items. (a) Is it appropriate to approximate the p distribution with a normal distribu- tion? Explain. (b) What are the values of u, and o ?
The table shows the results of rolling a fair six-sided die. Complete parts (a) through (d) below. Outcome on 100 100 Trials 500 Trials e Die Trials 1 20 18 75 2 14 21 84 3 13 20 89 4 15 14 72 19 15 85 19 12 95 (a) Using the table, find the empirical probability of rolling a 2 for the first 100 trials. The empirical probability of rolling a 2 for the first 100 trials is 0.14 . (Round to two decimal places as needed.) (b) Using the table, find the empirical probability of rolling a 2 for the second 100 trials. The empirical probability of rolling a 2 for second 100 trials is (Round to two decimal places as needed.)
Probability Scores 3 7 8 9 10 12 13 0.05 0.25 0.35 0.1 0.05 0.1 0.1 Find the expected value of the above random variable.
Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $150, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $140,000. g. What are the expected value and variance of your profit?
Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 1 2 3 4 5 Probability 0.259 0.293 0.244 0.150 0.037 0.017 ... (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.) The standard deviation is (Round to one decimal place as needed.) (b) Interpret the results. The mean is , so the average batch of 1000 machine parts has The standard deviation is so the typical number of defects in a batch of 1000 (Round to one decimal place as needed.)
The annual premium for a $20,000 insurance policy against the theft of a painting is $350. If the (empirical) probability that the painting will be stolen during the year is 0.02, what is your expected return from the insurance company if you take out this insurance? Let X be the random variable for the amount of money received from the insurance company in the given year. E(X)= dollars
ll 36 l 12% 7 15:04 4G .. Question One: (a) If 4 balanced coins are tossed simultaneously (or 1 balanced coin is tossed 4 times), compute the entire probability distribution and plot it. (b) Compute and plot the probability distribution for a sample of 5 items taken at random from a production process known to produce 30% defective items.
CLT for Proportions The proportion of taxpayers who file within 45 days of the tax season is 36.4%. 1. What is the proportion of taxpayers that file after 45 days? 2. If you randomly select 60 taxpayers, what is the probability that at least 40% file within 45 days? 3. If you randomly select 115 taxpayers, what is the probability that at most 35% file within 45 days? 4. If you randomly select 140 taxpayers, what is the probability that between 36% and 39% file within 45 days? 5. Describe this distribution (sample proportion) in statistical notation when n=90
Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 0 1 2 3 4 5 Probability 0.255 0.294 0.235 0.158 0.042 0.016 (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is enter your response here. (Round to one decimal place as needed.)
How do you find (b.) and (e.)??
Side-by-Side According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white in a 3 : I ratio. That is, cach plant has probability of having red blossoms, and the blossom colors of separate plants are independent. (c) What is the probability of obtaining at least 45 red-blossomed plants when 60 plants are grown from seeds? Use the Normal approximation. O 0.45 O 0.65 O 0.75 O 0.50
The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows: Procurement Cost ($) Probability Labor Cost ($) Probability Transportation Cost ($) Probability 10 0.25 20 0.10 3 0.75 11 0.45 22 0.25 5 0.25 12 0.30 24 0.35 25 0.30 Compute profit per unit for the base-case, worst-case, and best-case scenarios. Construct a simulation model to estimate the mean profit per unit. Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios? Management believes the project may not be sustainable if the profit per unit is less than $5. Use simulation to estimate the probability the profit per unit will be less than $5.

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