Question

A consumer organization estimates that over a 1 -year period 19% of cars will need to be repaired once, 7% will need repairs twice, and 1% will require three or more repairs. What is the probability that a car chosen at random will need no repairs? no more than one repair? some repairs? The probability that a car will require no repairs is The probability that a car will require no more than one repair is The probability that a car will require some repairs is

Answer 1

The probability that a car will require no repairs is 73%, the probability it will require no more than one repair is 92%, and the probability it will require some repairs is 27%.

Step-by-step explanation:

To calculate the probability that a car chosen at random will need no repairs, we can use the complementary probability of the car needing at least one repair. The probabilities given for one, two, and three or more repairs are 19%, 7%, and 1% respectively. To find the probability of no repairs, we subtract the sum of those probabilities from 100%:

Probability of no repairs = 100% - (19% + 7% + 1%) = 100% - 27% = 73%.

The probability that a car will require no more than one repair combines the probabilities of no repairs and exactly one repair:

Probability of no more than one repair = Probability of no repairs (73%) + Probability of exactly one repair (19%) = 73% + 19% = 92%.

The probability that a car will require some repairs is the complement of requiring no repairs, which is:

Probability of some repairs = 1 - Probability of no repairs = 1 - 73% = 27%.