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) =\(\large \frac{\frac{1}{5}.\frac{4}{100}}{\frac{1}{5} .\frac{4}{100}+\frac{1}{3}.\frac{5}{100}+\frac{7}{15}.\frac{15}{100}}\)
$\Rightarrow \large\frac{4/500}{4/500+5/300+7/100}$
$\Rightarrow \large\frac{4/500}{(12+25+105)/1500}$
$\Rightarrow \large\frac{4/500}{142/1500}$
$\Rightarrow \large\frac{6}{71}$