Step 1:

Given the total number of drivers are as follows: 3000 scooter drivers, 5000 car drivers and 7000 truck drivers.

Total = 3000+5000+7000 = 15000.

Step 2:

Let $E_1$ be the event that the insured person is a scooter driver.

P ($E_1$) = $\large\frac{\text{Number of scooter drivers}}{\text{Total number of drivers}}$

$\qquad=\large \frac{3000}{15000}$

$\qquad=\large \frac{1}{5}$

Step 3:

Let $E_2$ be the event that the insured person is a car driver.

P ($E_2$) = $\large\frac{\text{Number of car drivers}}{\text{Total number of drivers}} $

$\qquad=\large \frac{5000}{15000}$

$\qquad=\large \frac{1}{3}$

Step 4:

Let $E_3$ be the event that the insured person is a truck driver.

P ($E_3$) = $\large\frac{\text{Number of truck drivers}}{\text{Total number of drivers}}$

$\qquad=\large \frac{7000}{15000}$

$\qquad=\large \frac{7}{15}$

Step 5:

Let A: event that the insured person met with an accident.

P (scooter driver met w/ an accident) = P (A|$E_1$)

$0.04=\large\frac{4}{100}$

P (car driver met w/ an accident)= P (A|$E_2$)

$0.05=\large\frac{5}{100}$

P (truck driver met w/ an accident) = P (A|$E_3$)

$0.15=\large\frac{15}{100}$

Step 6:

The probability that a driver is a scooter driver who met w/ an accident is given by \(P(E_1/A)\).

We can use Baye's theorem, according to which $P(E_1|A) = \large\frac{P(E_1)(P(A|E_1)}{P(E_1)P(A|E_1) + P(E_2)P(A|E_2)+ P(E_3)P(A|E_3)}$

P ($E_1$|A) =\(\large \frac{\frac{1}{5}.\frac{4}{100}}{\frac{1}{5} .\frac{4}{100}+\frac{1}{3}.\frac{5}{100}+\frac{7}{15}.\frac{15}{100}}\)

$\Rightarrow \large\frac{4/500}{4/500+5/300+7/100}$

$\Rightarrow \large\frac{4/500}{(12+25+105)/1500}$

$\Rightarrow \large\frac{4/500}{142/1500}$

$\Rightarrow \large\frac{6}{71}$