An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table: Age of drivers (in years) Accidents in one year 0 1 2 3 Over 3 18-29 440 160 110 61 35 30-50 480 125 85 22 18 Above 50 360 45 35 15 9 If a driver is chosen at random from the city, find the probability for the driver being 30-50 years of age and having one or more accidents in one year
Question
An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table: Age of drivers (in years) Accidents in one year 0 1 2 3 Over 3 18-29 440 160 110 61 35 30-50 480 125 85 22 18 Above 50 360 45 35 15 9 If a driver is chosen at random from the city, find the probability for the driver being 30-50 years of age and having one or more accidents in one year
Solution
To find the probability of a driver being 30-50 years of age and having one or more accidents in one year, we need to consider the total number of drivers in the 30-50 age group who had one or more accidents, and divide it by the total number of drivers in the city.
From the given table, we can see that in the 30-50 age group, there are 480 drivers who had one accident, 125 drivers who had two accidents, 85 drivers who had three accidents, and 22 drivers who had more than three accidents.
To calculate the total number of drivers in the 30-50 age group who had one or more accidents, we add up these numbers: 480 + 125 + 85 + 22 = 712.
Now, we need to find the total number of drivers in the city. From the table, we can see that in the 18-29 age group, there are 440 drivers who had no accidents, 160 drivers who had one accident, 110 drivers who had two accidents, 61 drivers who had three accidents, and 35 drivers who had more than three accidents. In the above 50 age group, there are 360 drivers who had no accidents, 45 drivers who had one accident, 35 drivers who had two accidents, 15 drivers who had three accidents, and 9 drivers who had more than three accidents.
Adding up these numbers, we find that the total number of drivers in the city is: 440 + 160 + 110 + 61 + 35 + 480 + 125 + 85 + 22 + 360 + 45 + 35 + 15 + 9 = 2000.
Finally, we can calculate the probability by dividing the total number of drivers in the 30-50 age group who had one or more accidents (712) by the total number of drivers in the city (2000):
Probability = 712/2000 = 0.356
Therefore, the probability of a driver being 30-50 years of age and having one or more accidents in one year is 0.356, or 35.6%.
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