Please explain each step and write clear A consumer organiza

Please explain each step and write clear.

A consumer organization estimates that over a 1-year period 20% of cars will need to be repaired once, 10% will need to be repaired twice, and 5% will require three or more repairs. What is the probability that a car chosen at random will need,

(a) no repairs?

(b) no more than one repair?

(c) some repairs?

If you own three cars, what is the probability that,

(d) neither will need repairs?

(e) all three will need to be repaired twice?

(f) at least one car will need repairs?

(g) one will need to be repaired once, one will need to be repaired twice, and one will require three or more repairs?

Solution

a.) P(no repairs) = 1 - 0.20 - 0.10 - 0.05 = 0.65

b.) P(no more than 1 repair) = P(no repairs) + P(1 repair) = 0.65 + 0.20 = 0.85

c.) P(some repairs) = 1 - P(no repairs) = 1 - 0.65 = 0.35

d.) P(all 3 no repairs) = (0.65)^3 = 0.274625

e.) P(all 3 need repair twice) = (0.10)^3 = 0.001

f.) P(atleast one car need repairs) = 1 - P(all 3 no repairs) = 1 - (0.65)^3 = 0.725375

g.) P = 3C1*(0.20)(0.10)(0.05) = 3*(0.20)(0.10)(0.05) = 0.003