Homework SourseA study of automobile accidents produced the following resul
A study of automobile accidents produced the following results:
Probability of involvement in an accident during the first half of 2008:
(a) An accident report for the first half of 2008 is chosen at random. What is the probability that the Model year for the car in this accident is 2008?
(b) A motor vehicle registration at the N.J. Motor Vehicle Bureau is selected at random.What is the probability that the model year of the vehicle in this registration record is 2005 or older and it is not involved in any accident during the first half of 2008?
| Model Year | Proportion of all vehicles: | Probability of involvement in an accident during the first half of 2008: |
| 2006 | 0.16 | 0.05 |
| 2007 | 0.18 | 0.02 |
| 2008 | 0.20 | 0.01 |
| 2005 or older | 0.46 | 0.06 |
Solution
a.) P(accident) = (0.16)(0.05) + (0.18)(0.02) + (0.2)(0.01) + (0.46)(0.06) = 0.0412
SO P(2008|accident) = (0.2)(0.01)/(0.0412) = 0.04854
b.) P(2005 or older and no accident) = (0.46)(1-0.06) = (0.46)(0.94) = 0.4324
