5) Suppose the empirical probability of an accidental nuclear crisis on a given day is(3/18,250). Let's assume that a leader will launch a mistaken "retaliatory strike" 10% ofthe time when presented with an accidental nuclear crisis. Thus, given our assumptions,the probability of an accidental nuclear war on a given day is (3/182,500). Suppose thateach day is independent. Hence the passing of days is a sequence of independentBernoulli trials with p-(3/182,500). Let X be the number of days until an accidentalnuclear war.a) How is X distributed?a) What is the mean (u), variance(o), and standard deviation(o) of X?b) Convert the value, from part b, to years to obtain the expected number of years untilan accidental nuclear war.

Bernoulli Trail: In probability theory, a Bernoulli trial is a random experiment which has exactly…

Answered: 5) Suppose the empirical probability of…

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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Suppose an RMG production line is known to have 6.6 flaws (defects) in every 50 products. a. What is the probability that there will be 16 flaws (defects) in a batch of 100 products? Answer in exact fraction, or rounded to at least 4 decimal places. b. What is the probability that there will be more than 5 flaws (defects) in a particular batch of 50 products? Answer in exact fraction, or rounded to at least 4 decimal places.
A farmer has planted 12 new lemon trees of a special breed where the probability that the tree will give fruits the upcoming season is 0.7. What is the probability that less than 3 trees remain without fruits by the end of the upcoming season?
A hospital performs 6 complex surgeries of a certain type per week. It is known that 60% of patients undergoing a certain surgery survive. For 6 patients who will undergo surgery in one week, determine: (For items (a) to (d) consider rounding to the third decimal place, probabilities in the range [0,1] and tolerance of 0.01.For item (e) one decimal place will be considered and a tolerance of 0.1). a. The probability that at least 2 and at most 4 survive. b. What is the expected number of survivors among patients who will undergo surgery in one week?
A hospital performs 6 complex surgeries of a certain type per week. It is known that 60% of patients undergoing a certain surgery survive. For 6 patients who will undergo surgery in one week, determine: (For items (a) to (d) consider rounding to the third decimal place, probabilities in the range [0,1] and tolerance of 0.01.For item (e) one decimal place will be considered and a tolerance of 0.1). a. The probability that everyone survives. b. The probability that at least 4 survive. c. The probability that at most 5 survive.
5. Suppose that you know that your friend was born sometime in the year 2001, but not which day. Given this state of ignorance, we can model your friend's birthday as being chosen uniformly at random from the 365 days of a non-leap year. (In reality, these are not entirely uniform, but they're pretty close, and we can ignore this effect.) (a) What is the probability that your friend was born in January? (b) Suppose you remember that your friend's birthday is on the 20th (of some month). Conditioned on this fact, what is the probability that your friend was born in January? (c) Now suppose you remember that your friend's birthday is on the 30th (of soe month). Conditioned on this fact, what is the probability that your friend was born in January?
Suppose 50% of the registered voters in a country are Republican if a sample of 598 voters is selected what is the probability that the simple proportion of republicans will be greater than 47% round your answer to 4 decimal places
An insurance agent sells the policies to 20 persons having same age and in good health. Based on the company's record, the probability that person in this age will live for the next 20 years is 2/3. Find the probability (a) 8 persons, (b) at most 7 persons, (c) more than 7 persons, (d) at least 3 persons, (e) more than 6 persons but less than 11 persons are still alive at the end of this 20 years period. The probability for a mango tree from a certain type, will produce fruits in the first year is 0.8. Each time, the mango trees seller sells about 5 trees to the buyer with the guarantee that if less than 3 trees produce fruits in the first year, he will replace them according to the number of trees which do not produce fruits. (a) Calculate the probability that there will no replacement. (b) If he sells the trees to 3000 buyers that are 5 trees to each buyer, how many trees are expected to be replaced?
Instructor-created question Question Help A study of 420,051 cell phone users found that 132 of them developed cancer of the brain or nervous system. Complete parts (a) and (b). a. Use the sample data to construct a 90% confidence interval estimate of the percentage of cell phone uners who develop cancer of the brain or nervous system. (Round to three decimal places as needed.) b. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0247% tor those not using cell phones Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell phones? Why or why not? OA. No, because 0.0247% is included in the confidence interval OB. Yes, because 0.0247% is included in the confidence interval OC. No, because 0 0247% is not included in the confidence interval. OD. Yes, because 0.0247% is not included in the confidence interval nts
A law professor observed that only 20% of the students who get admitted to the freshmen class usually reached fourth year. Assuming that this is correct, find the probability that among 15 randomly selected first year students, exactly 3 students will reach fourth year?
Suppose one NBA player can get one point in each free shot with probability 0.8. Now he has five times of free shots and it is reasonable to assume that the result in each shot has no impact on other shots. (b) What is the probability of his getting 3 points?(c) What is the probability of his getting at least 2 points?(d) we define an unusual event if the chance of the event is below 5%. Is it an unusual event that he lost all his shots? please explain each step fully

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