a) A certain company sends 40% of its overnight mail parcels via express mail service E₁. Of these parcels,2% arrive after the guaranteed delivery time( L - the event late delivery). If a record of overnight mailing israndomly selected from the company's file, what is the probability that the parcel went via E, and was late?Suppose that 50% of the overnight parcels are sent via express mail E, and the remaining 10% are sent viaE3 Of those sent via E₂, only 1% arrive late, whereas 5% of the parcels handled by E, arrive late.b) What is the probability that a randomly selected parcel arrived late?c) If a randomly selected parcel has arrived on time, what is the probability that it was not sent via E₁.

Probability is the likelihood of the occurrence of an event. If an event is the occurrence based on…

Answered: a) A certain company sends 40% of its…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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8. A new computer virus can enter the system through e-mail or through the internet. Thereis a 30% chance of receiving this virus through e-mail. There is a 40% chance ofreceiving it through the internet. Also, the virus enters the system simultaneously throughe-mail and the internet with probability 0.15. What is the probability that the virus doesnot enter the system at all?
Detecting terrorists is a real problem, one that causes governments to spend millions per year. A particular surveillance system has been developed which correctly identifies a future terrorist 99% of the times and detects someone who is not a future terrorist 99.9% of times. Suppose that in a population of 300 million, there are 1000 potential/future terrorists. If one of these 300 million is randomly selected and scrutinized by the system, what is the probability that the person selected is actually a future terrorist? Also explain if the value of this probability makes you uncomfortable about using a surveillance system? Explain.
3. A retailer sells two brands of batteries that experience indicates are equal in demand. If he stocks two of each brand (which means he has 4 batteries in his store), what is the probability that a customer seeking to purchase two batteries, purchases the same brand? 1/3 2/3 01/2 1/4
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One student is selected at random from a group of 200 known to consist of 140 full-time (80 female and 60 male) student and 60 part-time (40 female and 20 male) students. Event A is "the student selected is full-time" and event C is "the student selected is female". (a) Are events A and C independent? (b) Find the probability of one student selected is full-time, that should be female.
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9. When Olympic athletes are tested for illegal drug use (i.e., doping), the result of a single test are used to ban the athlete from competition. In a population of 1,000 athletes, suppose 120 are illegally using testosterone. Of the users, suppose 66 would test positive for testosterone. Of the nonusers, suppose 11 would test positive.(a)Given that the athlete is a nonuser, find the probability that a drug test for testosterone will yield a negative result.(b)If an athlete tests positive for testosterone, find the probability that the athlete is really doping.
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