Part I: Sections 1.1- 1.53.Assume that 78% of all employees at Company ABC havehealth insurance through the company, while 64% have dental insurance.Additionally, suppose that 10% of all employees have neither health in-surance nor dental insurance through the company.What is the probability that a randomly selected employee(a)has both health insurance and dental insurance through the company?What is the probability that a randomly selected em-(b)ployee has dental insurance but not health insurace through the com-pany?

Answered: Part I: Sections 1.1-1.5 3. Assume that…

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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A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 90.2% for the medical students admitted through special programs. Be sure to enter at least 4 digits of accuracy for this problem! If 9 of the students from the special programs are randomly selected, find the probability that at most 6 of them graduated.P(at most 6) = At least 4 digits! Would it be unusual to randomly select 9 students from the special programs and get at most 6 that graduate? no, it is not unusual yes, it is unusual Would it be unusual to randomly select 9 students from the special programs and get only 6 that graduate? no, it is not unusual yes, it is unusual
If A and B are two mutually exclusive events with P(A)= 0.5 and P(B)=0.4, find the following probabilities: a) P(A \textrm{ and } B) = 0.5 b) P(A \textrm{ or } B) = c) P( \textrm{not }A ) = d) P( \textrm{not }B ) = 0.4 e) P( \textrm{not }(A \textrm{ or } B)) = 0.4 f) P( A \textrm{ and } (\textrm{not }B) ) =
11.) Upon arrival at a hospital emergency room, patients are categorized according to their conditions as critical, serious, or stable. In the past year: (i) 10% were critical (ii) 30% were serious (iii) the rest were stable (iv) 40% of critical patients died (v) 10% of serious patients died (vi) 1% of stable patients died Given that a patient survived, what is the probability that the patient was categorized as serious upon arrival? This is a Bayes' Theorem problems.
A disease afflicts 1 person in 10 in a population. A test for this disease results in 5% false positives. Assume that a random person is tested for the disease (this person is not selected for the test because there are other symptoms indicating the presence of the disease nor are there any special signs of being disease free). Assume that there are no false negatives from this test. A person tests positive. What is the probability that the person truly has the disease? Now assume that false negatives are 15%. What is the probability that the person truly has the disease? The following paragraph is taken from the National Cancer Institute’s web site on the PSA test for prostate cancer. The paragraph is the complete discussion of false positive PSA results offered on the web site.
A study considered risk factors for HIV infection among intravenous drug users [11]. It found that 40% of users who had ≤ 100 injections per month (light users) and 55% of users who had > 100 injections per month (heavy users) were HIV positive. A. Suppose we have a group of 10 light users and 10 heavy users. What is the probability that exactly 3 of the 20 users are HIV positive? B. What is the probability that at least 4 of the 20 users are HIV positive? Please show me the calculations by hand and not excel, I am trying to learn how to plug in these formulas myself and to solve without computer assistance. TY!
a) Mobile company Pear has established that mobile phone sales will increase in the next 6 months and that probability of such increase is 0.35. The probability that the interest rates on mobile financing loans will go up in the same period is estimated to be 0.70. The probability that mobile phone sales or interest rates will go up during the next 6 months is estimated to be 0.90. What is the probability that mobile phone sales will increase but interest rates will not during the next 6 months? Using probability rules, explain how you obtained the result.
A pathogen affects 1 person out of every 100 people. Suppose you come into contact with 40 randomly selected people in one day? 1. What is the probability that at least one of these 40 people is infected? 2. What is the probability that at least 2 out of the 40 randomly selected people are affected?
1. Assume your computer network may have been hacked and computers may have 2 different types of viruses (virus type-A and virus type-B). The current situation shows that 15% of computers end up with type-A virus, 10% end up with type-B virus, and 10% of the computers infected with type-A or type-B virus have both viruses. 1.a) Compute the probability that a computer is infected with both viruses 1.b) Compute the probability that a computer has type-B virus given that it has type-A virus
3. A study conducted at a large hospital found that 27.8 percent of all patients admitted to the hospital's ICU remained in the ICU for less than 24 hours. (A) If 8 patients are selected at random from the ICU patients at the hospital, what is the probability that 2 or fewer of them remained in the ICU for less than 24 hours? (B) Suppose that 20 patients are selected at random from the ICU patients at the hospital. Calculate the mean and standard deviation of the number of these patients who remained in the ICU for less than 24 hours. (C) Another result of the study was that for elective (non-emergency) admissions to the hospital's ICU, the length of the stay in the ICU had a mean of 18.9 hours and a standard deviation of 3.9 hours. Assuming that the length of stay in the ICU for elective admissions is normally distributed, what proportion of elective admissions remained in the ICU for less than 24 hours?

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