Question

На двух станках производится одна и та же деталь. Производительность одного станка 100 деталей в час, а другого – 80. Первый станок допускает 5% брака, а второй – 3%. С какой вероятностью изготовленная на этих станках деталь бракованная?

Answer 1

Допустим станки работали час.
тогда первый произвёл 100 деталей 5 из которых бракованные, а второй 80 деталей 2,4 из которых бракованные. всего у нас 180 деталей 7,4 из которых с браком. 7,4/180=0,0411 значит 4,1 % что случайно выбранная деталь окажется бракованной

Answer 2

Calculating the Probability of Defective Parts

To calculate the probability of producing a defective part on these two machines, we can use the following approach:

1. Calculate the Overall Defective Rate: - Machine 1 produces 100 parts per hour with a 5% defective rate. - Machine 2 produces 80 parts per hour with a 3% defective rate.

2. Calculate the Weighted Average Defective Rate: - We'll calculate the weighted average defective rate based on the production rates of the two machines.

3. Determine the Probability of Defective Parts: - Using the weighted average defective rate, we can determine the probability of producing a defective part.

Let's proceed with the calculations.

Calculations

1. Calculate the Overall Defective Rate: - Machine 1: 5% defective rate - Machine 2: 3% defective rate

2. Calculate the Weighted Average Defective Rate: - Weighted Average Defective Rate = ((Defective Rate Machine 1 * Production Rate Machine 1) + (Defective Rate Machine 2 * Production Rate Machine 2)) / (Total Production Rate) - Weighted Average Defective Rate = ((5% * 100) + (3% * 80)) / (100 + 80)

3. Determine the Probability of Defective Parts: - Probability of Defective Parts = Weighted Average Defective Rate / 100

Let's calculate the weighted average defective rate and the probability of producing a defective part.

Results

1. Calculate the Weighted Average Defective Rate: - Weighted Average Defective Rate = ((5% * 100) + (3% * 80)) / (100 + 80) - Weighted Average Defective Rate = (500 + 240) / 180 - Weighted Average Defective Rate = 740 / 180 - Weighted Average Defective Rate ≈ 4.11%

2. Determine the Probability of Defective Parts: - Probability of Defective Parts = Weighted Average Defective Rate / 100 - Probability of Defective Parts ≈ 4.11% / 100 - Probability of Defective Parts ≈ 0.0411

Conclusion

The probability of producing a defective part on these two machines is approximately 4.11%.