Question

Детали изготавливаются на 3 станках. Первый станок изготавливает 40% всей продукции, второй – 30%, третий – остальную часть. Вероятность брака первого станка -1%, второго – 2%, третьего – 3%. Найти вероятность того, что случайно выбранная деталь будет бракована

Answer 1

Ответ:

2%+1%=3%

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given three machines that produce parts, with each machine contributing a certain percentage to the total production. The first machine produces 40% of the total production, the second machine produces 30%, and the third machine produces the remaining portion. We are also given the probabilities of defects for each machine: 1% for the first machine, 2% for the second machine, and 3% for the third machine. We need to find the probability that a randomly selected part will be defective.

Solution

To find the probability that a randomly selected part will be defective, we need to consider the probabilities of defects for each machine and the contribution of each machine to the total production.

Let's calculate the probability step by step:

1. Calculate the weighted probability of defects for each machine: - The first machine produces 40% of the total production and has a defect probability of 1%. Therefore, the weighted probability of defects for the first machine is 40% * 1% = 0.4%. - The second machine produces 30% of the total production and has a defect probability of 2%. Therefore, the weighted probability of defects for the second machine is 30% * 2% = 0.6%. - The third machine produces the remaining portion, which is 100% - 40% - 30% = 30% of the total production. It has a defect probability of 3%. Therefore, the weighted probability of defects for the third machine is 30% * 3% = 0.9%.

2. Calculate the total weighted probability of defects by summing up the weighted probabilities of defects for each machine: - Total weighted probability of defects = weighted probability of defects for the first machine + weighted probability of defects for the second machine + weighted probability of defects for the third machine. - Total weighted probability of defects = 0.4% + 0.6% + 0.9% = 1.9%.

Therefore, the probability that a randomly selected part will be defective is 1.9%.

Conclusion

The probability that a randomly selected part will be defective is 1.9%.