Case study
Q17. The following data shows the number of the passengers vehicles drivers involved in
accidents for a particular city was obtained by selecting 2,000 drivers at random.
Age group
Number of
of drivers
accidents in
(In. Years)
one year
0 1 2 3 More
than 3
18-25 395 150 120 60 30
26-50 52070 70 25 25
Above 39040 10 10 15
50
find the probability of the following events for drivers selected at random from the city :-
1) being 18 to 25 years of age and having to accident in one year.
being 26 to 50 years of age and having two or more accidents in one year.
having no accidents in one yea
Answers
Answer:
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 year and having more accidents in a year.
= Total number of drivers = 2000
Number of trials = 2000
(1) The number of drivers having ages in 18 - 29 years and exactly 3 accidents in one year = 61.
Probability ( driver is 18 - 29 years old with exactly 3 accidents ) =
2000
61
.
(2) The number of drivers having ages in 30 - 50 years and with one or more accidents in one year = 125 + 60 + 22 + 18 = 225
Probability ( driver is 30 - 50 years old with with one or more accidents in one year ) =
2000
225
=
2
9
.
(3) The number of drivers having no accidents in one year = 440 + 505 + 360 = 1305
Probability ( number of drivers having no accidents in one year ) =
2000
1305
=
400
261
.