Heinrich matzinger

Georgia Tech Spring 2021 Heinrich Matzinger

Online Test 0 for math3670

Name: GT-number: Major:

0) Explain to a kid the Law of Large Number and why it holds. Write down your explanations. You will be asked to upload it independently of the test as a separate task. So, you take a fair six-sided die and throw many times and build the average....it is going to be approximately 3.5. Explain why this holds to a kid....

1) The probability that you are infected with a given illness is 10%. Let I designate the event that you are infected. (Only a blood test can reveal if you are infected, there are no visible symptoms). If you are infected and take a test, then the test has a 98% probability to detect that you are infected. If you are not infected the test always works correctly. Before doing a test, you have a 10% probability of being infected. Now, you do the test and the test tells you that you are not infected. After that test (given the result of the test), what is the probability that you are infected. Let N be the event that the test gave a negative (not-infected) result.

2) When you do not learn for an exam with Matzinger, the probability to get an f is 0.8. If you learn, the probability to get an f is 0.2. In Matzinger’s exams on the long run, there are 40% of students getting an f . Let F designate the event that a student (randomly chosen in Matzinger’s class) gets the grade f . Let NL be the event that this student did not learn for the test. Assuming we know that that student did get an f . What is the conditional probability, that he/she did not learn for that test?

3) Assume given an electrical network with 4 points and five segments between those points: the segment a goes from x to y, b goes from x to z, c goes from y to z and d goes from y to v whilst f goes from z to v. Each of the segments works independently form the others. Let A be the event that segment a works, let B be the event that segment b works,... Let pa be the probability that a works, hence pa = P (A). Let pb be equal to P (B),... We assume that pa, pb, pc, pd, pf are all given to us. Let E be the event that electricity can flow from x to v. Calculate P (E) in terms of pa, pb, pc, pd and pf . (HINT: use law of total probability. Consider the case when c is known to work and on other hand when c is known to not work....)

4) Same setting as in the previous problem. What is the (conditional) probability that segment c does not work, if we know that E holds (i.e. we know that electricity can flow from x to v. )(HINT: use Bayse rule....)

5) A cell phone company offers cell phone insurance for one year. If the cell phone breaks down completely, the company replaces it and this costs the company 500 dollars. This event has a probability of 5 percent, that is the cell phone will break down completely within a year with five percent probability. With ten percent probability the cell phone will need to be repaired and this will cost the company 100 dollars on average. Except these two cases, the cell phone will work and not cost the cell phone company anything. How much does the company need to charge for the one year cell phone insurance, excluding administrative and handling costs and excluding profit? Per year? Per month? Do yo think it is worth signing up for cell phone insurance?