Question

A consumer organization estimates that over a​ 1-year period 20​% of cars will need to be repaired​ once, 8​% will need repairs​ twice, and 2​% 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

Probability that a car need to be repaired​ once = 20% = 0.20

Probability that a car need to be repaired​ twice = 8% = 0.08

Probability that a car need to be repaired​ three or more = 2% = 0.02

a) If you own two​ cars what is the probability that neither will need​ repair?

Probability that a car need to be repaired​ once , twice and thrice or more= 0.20+0.08+0.02=0.3

Probability that car need no repair = 1-0.3=0.7

Neither car will need repair=
`0.7 * 0.7=0.49`

​b) both will need​ repair?

Probability both will need​ repair =
`0.3 * 0.3=0.09`

c)at least one car will need​ repair

Neither car will need repair=
`0.7 * 0.7=0.49`

Probability that at least one car will need​ repair= 1-0.49 = 0.51