1. A firm rents out cars and operates from three locations - the Airport, the Beach and the City. Customers may return vehicles to any of the three locations. The company estimates that the probability of a car being returned to each location is as follows: Airport Car returned to Car hired from Airport Beach City 12 13 14 13 12 34 13 H4 4 4 AF Beach City Figure 1: Table of car-hire data. 0 (a) A car is currently parked in the city. What is the probability that, after being hired three times, it ends up in the city? [2 marks] (b) A car is parked at the airport. On average, how many times will it need to be hired until it is left in the city? [2] (c) The firm has been running for many years with a fleet of 25 cars, of which 10 are currently on hire. How many of the other cars would you expect to be parked at each of the three locations? Explain your answer clearly. [4] (d) Due to a coding error an intern accidentally inverts the list of dates of hire for the last year (so the most recent hire now looks like the first hire and the first hire looks like the most recent). The intern says nothing and hopes nobody will notice, will they be caught? Justify your answer. [2]

1. A firm rents out cars and operates from three locations - the Airport, the Beach and the City. Customers may return vehicles to any of the three locations. The company estimates that the probability of a car being returned to each location is as follows: Airport Car returned to Car hired from Airport Beach City 12 13 14 13 12 34 13 H4 4 4 AF Beach City Figure 1: Table of car-hire data. 0 (a) A car is currently parked in the city. What is the probability that, after being hired three times, it ends up in the city? [2 marks] (b) A car is parked at the airport. On average, how many times will it need to be hired until it is left in the city? [2] (c) The firm has been running for many years with a fleet of 25 cars, of which 10 are currently on hire. How many of the other cars would you expect to be parked at each of the three locations? Explain your answer clearly. [4] (d) Due to a coding error an intern accidentally inverts the list of dates of hire for the last year (so the most recent hire now looks like the first hire and the first hire looks like the most recent). The intern says nothing and hopes nobody will notice, will they be caught? Justify your answer. [2]

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 85E

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