Questions: An actuary studied the likelihood that different types of drivers have at least one collision during any one-year period. The results of the study appear below. Teen 140 Young adult 102 Middle aged adult 82 Senior 168 Find the probability that a driver with at least one collision in the past year is a Senior driver. Please enter your answer as a decimal to three decimal places.

An actuary studied the likelihood that different types of drivers have at least one collision during any one-year period. The results of the study appear below. Teen 140 Young adult 102 Middle aged adult 82 Senior 168 Find the probability that a driver with at least one collision in the past year is a Senior driver. Please enter your answer as a decimal to three decimal places.
Transcript text: An actuary studied the likelihood that different types of drivers have at least one collision during any one-year period. The results of the study appear below. Teen 140 Young adult 102 Middle aged adult 82 Senior 168 Find the probability that a driver with at least one collision in the past year is a Senior driver. Please enter your answer as a decimal to three decimal places.
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Solution

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Solution Steps

Step 1: Identify the given data

The table provides the number of drivers with at least one collision in the past year for each age group. Specifically:

  • Teen: 140 collisions
  • Young adult: 102 collisions
  • Middle-aged adult: 82 collisions (out of 1260 total drivers)
  • Senior: 168 collisions (out of 4018 total drivers)
Step 2: Calculate the total number of drivers with at least one collision

To find the total number of drivers with at least one collision, sum the collisions across all age groups: \[ \text{Total collisions} = 140 + 102 + 82 + 168 = 492 \]

Step 3: Calculate the probability that a driver with at least one collision is a Senior driver

The probability \( P \) that a driver with at least one collision is a Senior driver is given by: \[ P = \frac{\text{Number of Senior drivers with at least one collision}}{\text{Total number of drivers with at least one collision}} \] Substitute the values: \[ P = \frac{168}{492} = 0.3415 \] Rounding to three decimal places: \[ P \approx 0.342 \]

Final Answer

The probability that a driver with at least one collision in the past year is a Senior driver is \(\boxed{0.342}\).

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