maths exerciseto help with probability, Exercises of Macroeconomics

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7Let X be the number of people that the doctor sees who have the virus. X-B (80, 0.8%) a P(X =2) —0.108 (2 s.f.) b P(X > 3) = 0.0267 (3 s.f.) ¢ It is assumed that the patients will or will not have the virus independently of each other; in reality, if the prevalence nationwide is 0.8%, it is likely that there will be geographical pockets that are higher and lower than this, since a cold virus is contagious. Therefore if the doctor sees one patient with the virus, it may be supposed that the virus is prevalent in the locality, so the probability of seeing other patients with the virus will be higher than 0.8%. It is also assumed that the country is large enough that the doctor will not be seeing a significant fraction of the whole population; an island nation of a few hundred, for example, would not allow for a binomial model to be used for a sample of 80, for the same reasons as outlined in Question 5a. However, given the context of the question, this would not be the answer the examiner would be looking for. 8Let X be the number of sixes in four throws: X-B (« 3) . P(X = 3) = 0.0154 (3 s.f.) Let ¥ be the number of fives or sixes in six throws: Y-B (6 ) P(¥ =5) = 0.0165 (2 s.f.) Rolling five fives or sixes in six throws is the more probable.