Covid-19 ward nurses worry about the number of arriving patients in their ward. In a typicalhospital, the nurses cannot accept arriving patients if there are more than 10 Covid-19 cases in agiven hour. It is assumed that patient's arrival follows a Poisson process, and historical datasuggest that, on the average, 5 cases arrive per hour.What is the probability that in every two hours the nurses cannot accommodate the arrivingpatients?a. 0.4170O b. NONEO c. 0.5830d. 0.0137 Walmark randomly draws 5 different gift vouchers to be given to selected loyal customers eachday. For today, they draw the $5 gift voucher. What is the expected number of days until this giftvoucher is again drawn? What is the probability that this gift voucher is again drawn exactly 5days from now? Let X denote a geometric random variable. (Show solutions)O a. E(X) = 10 days, P(X-5) = 0.0819O b. NONEc. E(X) = 5 days, P(X-5) = 0.0819O d. E(X) = 5 days, P(X-5) = 0.0656

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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...

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1. (Witmer book – Page 116, Q: 3.6.12) Childhood lead poisoning is a public health concern in the United States. In a certain population, 1 child in 8 has a high blood lead level (defined as 30 µg/dl or more). In a randomly chosen group of 16 children from the population, what is the probability that a. None has high blood lead? b. 1 has high blood lead? c. 2 have high blood lead? d. 3 or more have high blood lead? Hint: Use parts a – c to help you answer.
TABLE 4.6 Sneakers are no longer just for the young. In fact, most adults own multiple pairs of sneakers. Table 4.6 gives the fraction of U.S. adults 20 years of age and older who own five or more pairs of wearable sneakers, along with the fraction of the U.S. adult population 20 years or older in each of five age groups. Use the Law of Total Prob- ability to determine the unconditional probability of an adult 20 years and older own- ing five or more pairs of wearable sneakers. 6 Probability Table Groups and Ages G3 35-49 Fraction with ≥ 5 Pairs .13 Fraction of U.S. Adults 20 and Older .30 G₁ 20-24 26 .09 G₂ 25-34 .20 .18 G4 50-64 18 .25 G5 ≥ 65 .14 .18 AI
Q. 2 A car dealer notes the following probabilities about his customers: P(those who buy a new car) = 0.25 P(those who buy a European car) = 0.30 P(those who neither buy a new car nor an European car) = 0.54 Find the probability that next customer buys a new European car?
The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40 machines are selected at random, the probability that 38 or more will not develop any faults within the first 3 years of use is ....
Q. 1 It is estimated that 80% of emails are spam emails. Some software has been applied to filter these spam emails before they reach our inbox. A certain brand of software claims that it can detect 99% of spam emails, and the probability for a false positive (a non-spam email detected as spam) is 5%. Now if an email is detected as spam, then what is the probability that it is in fact a non-spam email? event A: email is spam; event B: email is detected as spam. Assume that
A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.95 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes. (a) Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods. = (b) What is the probability that in the long run the traffic will not be in the delay state? (Enter your probabilities as fractions.) No Traffic Delay Traffic Delay π 1 =…
The management of the large department store in Example B.1 must determine whether more training is neededfor the customer service clerk. The clerk at the customer service desk can serve an average of three customersper hour. What is the probability that a customer will require 10 minutes or less of service?
Suppose that on any given day, there is a 20% chance that Lebron has a bad day, a 50% day that Lebron has a so-so day, and a 30% chance that Lebron has a good day. On a bad day, the probability that Lebron makes any given 3-point shot is 0.5. On a so-so day, the probability that Lebron makes any given 3-point shot is 0.7. On a good day, the probability that Lebron makes any given 3-point shot is 0.9. Suppose that tomorrow, Lebron takes a 3-point shot, and we record whether he hits or misses and what kind of day he was having. What is the probability that Lebron hits? What is the probability that if Lebron is having a bad day given that he misses a shot that day?
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 7 customers per hour and an average service rate of 12 customers per hour. The probability of 2 customers in the system is : a. 0.1418 b. 0.6597 C. 0.4167 d. 0.8582

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