Question

A car manufacturing plant assembles 26 cars with 7 having bad brakes. a random inspection reviews 4 cars' brakes. what is the probability that all the cars chosen have good brakes? round to the nearest thousandths.

Answer 1

The probability that all the cars chosen have good brakes is approximately 0.371.

Step-by-step explanation:

To find the probability that all the cars chosen have good brakes, we need to calculate the probability of choosing a car with good brakes for each of the 4 cars inspected.

Given that there are 26 total cars with 7 having bad brakes, there are 19 cars with good brakes. So, the probability of choosing a car with good brakes for the first inspection is 19/26.

Since the inspections are done randomly and we're assuming that each inspection is independent, the probability of choosing a car with good brakes for each subsequent inspection is also 19/26.

Therefore, the overall probability of choosing 4 cars with good brakes is (19/26) * (19/26) * (19/26) * (19/26) ≈ 0.371.

Answer 2

The probability that all four randomly chosen cars have good brakes from a lot where 7 out of 26 cars have bad brakes is calculated using the hypergeometric distribution formula, considering combinations of selecting 4 good cars out of 19, over the total combinations of choosing any 4 out of 26.

Step-by-step explanation:

The question asks to calculate the probability that all cars chosen have good brakes during a random inspection of 4 cars from a lot of 26, where 7 cars have known bad brakes. To find this probability, we assume that the event of choosing each car is independent and use the hypergeometric distribution formula.

Firstly, let's determine the number of ways to choose 4 cars with good brakes from the 19 that are good (26 total - 7 with bad brakes). That would be the combination of 19 taken 4 at a time, which is denoted as C(19, 4).

Next, we'll calculate the total number of ways to choose any 4 cars from the 26, which is C(26, 4).

The probability is then the ratio of these two values:

Probability = C(19, 4) / C(26, 4)

After calculating these combinations, we find the probability and round it to the nearest thousandths as instructed.