Question

A consumer organization estimates that over a​ 1-year period 20​% of cars will need to be repaired​ once, 9​% will need repairs​ twice, and 4​% will require three or more repairs. If you own two​ cars, what is the probability that ​a) neither will need​ repair? ​b) both will need​ repair? ​c) at least one car will need​ repair?

Answer 1

Explanation:

Given that a consumer organization estimates that over a​ 1-year period 20​% of cars will need to be repaired​ once, 9​% will need repairs​ twice, and 4​% will require three or more repairs.

No of cars -2

Each car is independent of the other.

Prob that a car does not need repair
`= 1-0.20-0.09-0.04 = 0.67`

a) Prob (neither will need repair) =
`0.67*0.67=0.4489`

b) Prob (both will need repair) =
`0.33*0.33=0.1089`

c) Prob (atleast one will need repair) =1- neither repair

=1-0.4489

=0.5511