An insurance company classifies drivers as low-risk, medium-risk and high-risk. Of those insured, 60% are low-risk, 30% are medium-risk and 10% are high-risk. After a study, the company finds that during a 1-year period, 1% of the low-risk drivers had an accident, 5% of the medium-risk drivers had an accident and 9% of the high-risk drivers had an accident.

If two drivers who had an accident during the 1-year period are selected, what is the probability that at least one of them has been classified as high-risk?

Answer: 0.51

How to arrive at this answer???

Want solution

To find the probability that at least one of the two drivers who had an accident during the 1-year period is classified as high-risk, you can use the complement rule. The complement of "at least one driver is high-risk" is "neither driver is high-risk."

To calculate this probability, follow these steps:

Step 1: Calculate the probability of neither driver being high-risk.

The probability that the first driver selected is not high-risk is 1 - 0.10 (probability of being high-risk) = 0.90.
The probability that the second driver selected is also not high-risk is also 0.90.
So, the probability that neither driver is high-risk is (0.90) × (0.90) = 0.81.

Step 2: Calculate the complement of this probability.

The complement of the probability that neither driver is high-risk is 1 - 0.81 = 0.19.

Therefore, the probability that at least one of the drivers is classified as high-risk is 1 - 0.19 = 0.81 (or 81%).

To find the probability that at least one of the selected drivers has been classified as high-risk, we can use the complement rule.

First, let's find the probability that neither of the selected drivers has been classified as high-risk.

The probability of selecting a low-risk driver who had an accident is 0.60 * 0.01 = 0.006.
The probability of selecting a medium-risk driver who had an accident is 0.30 * 0.05 = 0.015.

Now, let's find the probability of selecting two drivers who had an accident but none of them are classified as high-risk.
Since the events of selecting a low-risk driver and a medium-risk driver are independent, we can simply multiply their probabilities:
0.006 * 0.015 = 0.00009.

Next, we will find the complement of this probability, which is the probability that at least one of the selected drivers has been classified as high-risk.
The complement of an event, A, is equal to 1 - P(A).

So, the probability that at least one of the selected drivers has been classified as high-risk is:
1 - 0.00009 = 0.99991.

Therefore, the probability that at least one of the selected drivers has been classified as high-risk is approximately 0.99991.

However, since the question asks for the answer rounded to two decimal places, the answer is 1.00.