An insurance company insured 1500 scooter drivers, 2500 car drivers and 4500 truck drivers. The probability of a scooter, a car and a truck meeting with an accident is 0.01, 0.02 and 0.04 respectively. If one of the insured persons meets with an accident, find the probability that he is a scooter driver.

Answer

To find the probability that a person who meets with an accident is a scooter driver, we can use Bayes' theorem. Let's denote the events as follows:

- Let \( S \) be the event that the person is a scooter driver.
- Let \( C \) be the event that the person is a car driver.
- Let \( T \) be the event that the person is a truck driver.
- Let \( A \) be the event that the person meets with an accident.

We need to find \( P(S | A) \), the probability that the person is a scooter driver given that they have met with an accident.

### Step 1: Calculate the total number of insured drivers
The total number of insured drivers is:
\[ N = 1500 + 2500 + 4500 = 8500 \]

### Step 2: Calculate the number of accidents for each type of driver
- The number of scooter drivers who meet with an accident:
\[ N(S \cap A) = 1500 \times 0.01 = 15 \]
- The number of car drivers who meet with an accident:
\[ N(C \cap A) = 2500 \times 0.02 = 50 \]
- The number of truck drivers who meet with an accident:
\[ N(T \cap A) = 4500 \times 0.04 = 180 \]

### Step 3: Calculate the total number of accidents
The total number of accidents is:
\[ N(A) = N(S \cap A) + N(C \cap A) + N(T \cap A) = 15 + 50 + 180 = 245 \]

### Step 4: Apply Bayes' theorem
Now, we can use Bayes' theorem to find \( P(S | A) \):
\[ P(S | A) = \frac{P(A | S) \cdot P(S)}{P(A)} \]
Where:
- \( P(A | S) = 0.01 \) (the probability of an accident given that the person is a scooter driver)
- \( P(S) = \frac{1500}{8500} \) (the prior probability of being a scooter driver)
- \( P(A) = \frac{N(A)}{N} = \frac{245}{8500} \) (the total probability of an accident)

### Step 5: Substitute the values
Substituting the values into Bayes' theorem:
\[ P(S | A) = \frac{0.01 \cdot \frac{1500}{8500}}{\frac{245}{8500}} \]

### Step 6: Simplify the expression
\[ P(S | A) = \frac{0.01 \cdot 1500}{245} \]
\[ P(S | A) = \frac{15}{245} \]
\[ P(S | A) = \frac{3}{49} \]

### Final Answer
Thus, the probability that a person who meets with an accident is a scooter driver is:
\[ \boxed{\frac{3}{49}} \]