Question

An auto dealer sold 135 hybrid cars. His records show that the following repairs were required during the first year. Repair Frequency Minor 63 Major 23 No repairs 49 Mrs. Slegh purchases a hybrid car from the dealer. Find the probability that she will return during the first year for the following. (Round your answers to three decimal places.) (a) minor repairs (b) major repairs (c) no repairs

Answer 1

(a) Probability of minor repairs ≈ 0.467

(b) Probability of major repairs ≈ 0.170

(c) Probability of no repairs ≈ 0.363

Explanation:

To find the probability for each case, you need to use the given data on repair frequency. Let's calculate each probability:

(a) Probability of minor repairs:

To find the probability of minor repairs, you need to divide the number of cars that required minor repairs (63) by the total number of cars sold (135).

Probability of minor repairs = Number of cars with minor repairs / Total number of cars sold

Probability of minor repairs = 63 / 135

Now, calculate this probability:

Probability of minor repairs ≈ 0.467 (rounded to three decimal places)

(b) Probability of major repairs:

To find the probability of major repairs, you need to divide the number of cars that required major repairs (23) by the total number of cars sold (135).

Probability of major repairs = Number of cars with major repairs / Total number of cars sold

Probability of major repairs = 23 / 135

Now, calculate this probability:

Probability of major repairs ≈ 0.170 (rounded to three decimal places)

(c) Probability of no repairs:

To find the probability of no repairs, you need to divide the number of cars with no repairs (49) by the total number of cars sold (135).

Probability of no repairs = Number of cars with no repairs / Total number of cars sold

Probability of no repairs = 49 / 135

Now, calculate this probability:

Probability of no repairs ≈ 0.363 (rounded to three decimal places)

So, the probabilities are as follows:

(a) Probability of minor repairs ≈ 0.467

(b) Probability of major repairs ≈ 0.170

(c) Probability of no repairs ≈ 0.363

Answer 2

To find the probability, we need to divide the number of favorable outcomes (the number of times Mrs. Slegh will return for each type of repair) by the total number of possible outcomes (the total number of hybrid cars sold).

(a) Probability of minor repairs:

The number of minor repairs is given as 63.

Total number of hybrid cars sold is 135.

Probability of minor repairs = Number of minor repairs / Total number of hybrid cars sold

Probability of minor repairs = 63 / 135 ≈ 0.467

(b) Probability of major repairs:

The number of major repairs is given as 23.

Total number of hybrid cars sold is still 135.

Probability of major repairs = Number of major repairs / Total number of hybrid cars sold

Probability of major repairs = 23 / 135 ≈ 0.170

(c) Probability of no repairs:

The number of no repairs is given as 49.

Total number of hybrid cars sold is 135.

Probability of no repairs = Number of no repairs / Total number of hybrid cars sold

Probability of no repairs = 49 / 135 ≈ 0.363

Therefore, the probabilities are:

(a) Probability of minor repairs ≈ 0.467

(b) Probability of major repairs ≈ 0.170

(c) Probability of no repairs ≈ 0.363