The time that it takes to service a car is an exponential random variable with rate 1. 1. If A brings his car in at time 0 and B brings his car in at time t, what is the probability that B’s car is ready before A’s? Assume that the service times are independent, and the service begins upon arrival. 2. If both cars are brought in at time 0, with work starting on B’s car only when A’s car has been completely serviced, what is the probability that B’s car is ready before 2?

The time that it takes to service a car is an exponential random variable with rate 1. 1. If A brings his car in at time 0 and B brings his car in at time t, what is the probability that B’s car is ready before A’s? Assume that the service times are independent, and the service begins upon arrival. 2. If both cars are brought in at time 0, with work starting on B’s car only when A’s car has been completely serviced, what is the probability that B’s car is ready before 2?

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

In the game of roulette, a player can place a $9 bet on the number 29 and have a probability of winning. If the metal ball lands on 29, the player gets to keep the 38 1 $9 paid to play the game and the player is awarded an additional $315. Otherwise, the player is awarded nothing and the casino takes the player's $9, Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. The expected value is $.5 (Round to the nearest cent as needed.)
Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .
Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is bbg, then R(bbg) = 1. Suppose that the random variable X is defined in terms of R as follows: X=R- - 2R-4. The values of X are given in the table below. Outcome bbb ggb bbg gbg gbb bgg bgb gg Value of X-4 -4 -5 -4 -5 -4 -5 -1 Calculate the values of the probability distribution function of X, i.e. the function py. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X Px (x) E 1:48 PM 3/21/2022 hp Compag LAI956X 立
The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.
Assume that the batter hits with probability 0.2 against left-handed pitchers, and with probability 0.3 against right-handed pitchers. Both situations are Bernoulli processes. One month the player bats 22 times against left-handed pitchers and 52 times against right-handed pitchers. How many hits should the batter expect to get during this month?
Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?
According to recent reports, currently 39% of the population of NC (adults and children) has been fully vaccinated against Covid. Suppose of random sample of 400 individuals from the population of NC is selected. Let x represent the number in the sample who are fully vaccinated. d. Find the probability that 130 or fewer in the sample have been fully vaccinated. Round to 4 decimal places. Would this result be unusual? Explain.
Two professors are applying for grants. Professor Jane has a probability of 0.66 of being funded. Professor Joe has probability 0.29 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent.Give your answer to four decimal places. 1. Given at least one of the professors is funded, what is the probability that Professor Jane is funded, but Professor Joe is not?
T1.4 Suppose that 30% of all people who buy a new Iphone also buy an Apple watch. Consider randomly selecting 20 people who bought a new Iphone, and let X be the number of those who also bought an Apple watch. a) Find the probability that at least 6 of them bought an Apple watch. b) Find the probability that between 4 and 10 of them, inclusive, bought an Apple watch.
A bank has 3 counter desks and a very large waiting lounge (assume infinite queue). Customers arrive with a mean of 20 per hour and each desk serves with mean 10 customers per hour, where both rates are exponential. Determine the following : (a) Determine An, tn, C, and Aeff for n = 0, 1, 2, 3... (b) The steady-state probabilities pn,n = 0, 1, 2, 3.. (c) Calculate steady-state measures Ls, Ws, Lg, Wq, c and utilization ratio.
You're a production engineer for a small manufacturing facility that contains three machines (M1, M2, M3) that are arranged in series. That is, raw material enters M, and leaves M3 as a finished part. Time between failures (in days) for machine M; is described with random variables T;, which are assumed to follow exponential distributions with the parameters found in the table below. The reliability, R;(t), or the probability that failure occurs after time t, of Mi is calculated as 1 - F;(t). And recall that F;(t) is the cumulative probability distribution for Mi evaluated at time t. a. Calculate the average failure time for the three machines. b. Calculate R;(14), or reliability at 14 days of operation, for each machine. Calculate the system reliability, Rs(14), for this series system (that is, the probability that raw material can enter M, and leave M3, at 14 days of operation). с. M1 М M3 M1 M2 M3 0.026 0.012 0.019
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…