Let E1,E2 and E3 be the events of a driver being a scooter driver, car driver and truck driver respectively. Let A be the event that the person meets with an accident.
There are 2000 insured scooter drivers, 4000 insured car drivers and 6000 insured truck drivers.
Total number of insured vehicle drivers = 2000 + 4000 + 6000 = 12000
∴ P(E1) =

2000

12000

=

1

6

, P(E2) =

4000

12000

=

1

3

, P(E3) =

6000

12000

=

1

2

Also, we have:
P (A|E1) = 0.01 =

1

100

P (A|E2) = 0.03 =

3

100

P (A|E3) = 0.15 =

15

100

Now, the probability that the insured person who meets with an accident is a scooter driver is P (A|E1).
Using Bayes’ theorem, we obtain:
P (E1|A) =
=

1 6 × 1 100

1 6 × 1 100 + 1 3 × 3 100 + 1 2 × 15 100

=

1 6

1 6 +1+ 15 2

=

1

6

×

6

52

=

1

52