(a) Every working day, Alan reverses his car from his driveway on to the road in such a waythat there is a very small probability p that his car will be involved in a collision.(i) Show that the probability that there will be no collision in a five-day week is (1– p)³.(ii) State one assumption that is made in your answer above.(iii) Let p0.001. Check that the Poisson approximation can be used, and find theapproximate probability that Alan will avoid a collision in 500 working days. Roundyour answer to 4 decimal places.(b) Organisms are present in ballast water discharged from a ship according to a Poisson pro-cess with a concentration of 4 organisms per cubic meter. Find the probability that thenumber of organisms in 1.5 cubic meter of discharge exceeds its mean value by more thanone standard deviation. Round your answer to 4 decimal places.(c) The number of times that a person gets a cold in a given year is a Poisson random variablewith parameter A = 5. Suppose that a new supplement which has just been marketedreduces the Poisson parameter to A = 3 for 75% of the population. For the other 25% ofthe population, the supplement gives no significant reduction on the number of colds. If anindividual tries the supplement for a year and has 2 colds in that time, find the conditionalprobability that the supplement is beneficial for him or her. Round your answer to 4 decimalplaces.

(a)I GIVEN Alan reverses his car from his driveway in the road in such a way that there is a very…

(i) Show that the probability that there will be no collision in a five-day week is (1 – p)°. (ii) State one assumption that is made in your answer above. (iii) Let p = 0.001. Check that the Poisson approximation can be used, and find the approximate probability that Alan will avoid a collision in 500 working days. Round

(i) Show that the probability that there will be no collision in a five-day week is (1 – p)°. (ii) State one assumption that is made in your answer above. (iii) Let p = 0.001. Check that the Poisson approximation can be used, and find the approximate probability that Alan will avoid a collision in 500 working days. Round

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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