# Joint probability

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Newspaper article frequently cite the fact that in any one year a small percentage (say 10%) of all drivers are responsible for all automobile accidents. The conclusion is often reached that if only we could single out these accident-prone drivers and either retrain them or remove them from the reads we could drastically reduce auto accidents. You are told that of 100,000 drivers who are involved in one or more accidents in one year, 11,000 of them were involved on one or more accidents the next year

Given the above information complete the entries in the joint probability table below

First Second

Year year Accident No Accident Marginal probability

Of event in prior year

Accident .10

No Accident .90

Marginal probability of event in second year .10 .90 1.00

b) Is searching for accident-prone drivers is an effective way to reduce auto accidents? Explain

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#### Solution Preview

Row 1, column 1:

probability that a driver involved in one or more accident this year will have the chance of accident in next year

p(AA) = 0.1*(11000/100000) = 0.1*0.11= 0.011 --Answer

Row 1, column 2:

probability that a driver involved in one or more accident this year will not be involved ...

#### Solution Summary

This shows how to complete a joint probability table. The marginal probability of event in second year are found.