An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained is given in the following table:

Question

An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained is given in the following table:

Find the probabilities of the following events for a driver chosen at random from the city:

i. The driver being in the age group 18-29 years and having exactly 3 accidents in one year.

ii. The driver being in the age group of 30-50 years and having one or more accidents in a year.

iii. Having no accidents in the year.

Philoid · Accepted Answer

here, sample space = 2000 being drivers selected at random

i) Given that the driver belongs to the age group of 18-29 and have exactly 3 accidents in one year

Let E be the event of selecting the driver from this age group with exactly having 3 accidents in a year

So the possible outcomes will consist 61

∴ P ( E) =

ii.) Here the chances of choosing a driver from age group of

30 -50 and having 1 or more than 1 accident in a year will be total number of drivers meeting 1 or more than 1 accidents in a year

⇒ 125 + 60 + 22 + 18 = 225

Let E be the event of choosing the driver from this age group meeting more than 1 accident in a year

∴ P (E) =

iii.) let E be the event of choosing a driver who haven’t meet any accident in a year

The age group Is not mentioned so we will add all the age group drivers who haven’t meet any accident in the year

The number of drivers (favorable outcome)

= 440 + 505 + 360 = 1305

∴