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.
Answers
Answer:
0.0305, 0.1125, 0.6525
Step-by-step explanation:
Given that insurance company selected 2000 drivers at random.
∴ Total number of drivers, n(S) = 2000.
(i)
Let A be the event of choosing a driver being 18-29 years and having exactly 3 accidents in one year.
A = The number of drivers having ages in 18-29 and 3 accidents in 1 year = 61.
n(A) = 61.
∴ Required probability P(A) = n(A)/n(S) = 61/2000 = 0.0305.
(ii)
Let B be the event of choosing the drivers whose are being in the age group of 30-50 years and having one or more accidents.
B = 125 + 60 + 22 = 225.
n(B) = 225.
∴ Required probability p(B) = n(B)/n(S) = 225/2000 = 0.01125
(iii)
Let C be the event of choosing a driver having no accidents in the year.
C = 440 + 505 + 360 = 1305
n(C) = 1305.
∴ Required probability P(C) = n(C)/n(S) = 1305/2000 = 0.6525.
Hope it helps!
Step-by-step explanation:
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.
P( driver is 18 - 29 years old with exactly 3 accidents ) = 61 / 2000 .
(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
P( driver is 30 - 50 years old with with one or more accidents in one year ) = 225 / 2000 = 45 / 400 = 9 / 80 .
(3) The number of drivers having no accidents in one year = 440 + 505 + 360 = 1305
P( number of drivers having no accidents in one year ) = 1305 / 2000 = 261 / 400 .