Question

На сборку попадают детали с трех автоматов. Известно, что первый автомат дает 0,2% брака, второй – 0,3%, третий – 0,4%. Найдите вероятность попадания на сборку бракованной детали, если с первого автомата поступило 500, со второго – 1000 и с третьего – 1500 деталей.

Answer 1

1) 500*0,4/100 = 2%
2) 1000*0,2/100=2%
3) 1250*0,6/100=7.5%
2/100 + 2/100 + 7.5/100 = 0.115
наверное так

Answer 2

Calculation of the Probability of Defective Parts

To calculate the probability of receiving defective parts on the assembly line, we need to consider the defect rates of each machine and the number of parts received from each machine.

Let's denote the defect rates of the three machines as follows: - Machine 1: 0.2% - Machine 2: 0.3% - Machine 3: 0.4%

And let's denote the number of parts received from each machine as follows: - Machine 1: 500 parts - Machine 2: 1000 parts - Machine 3: 1500 parts

To find the probability of receiving defective parts, we can calculate the weighted average of the defect rates based on the number of parts received from each machine.

The calculation can be done as follows:

Probability of receiving defective parts = (Defect rate of Machine 1 * Number of parts from Machine 1 + Defect rate of Machine 2 * Number of parts from Machine 2 + Defect rate of Machine 3 * Number of parts from Machine 3) / Total number of parts received

Substituting the given values:

Probability of receiving defective parts = (0.002 * 500 + 0.003 * 1000 + 0.004 * 1500) / (500 + 1000 + 1500)

Simplifying the calculation:

Probability of receiving defective parts = (1 + 3 + 6) / 3000

Probability of receiving defective parts = 10 / 3000

Probability of receiving defective parts = 0.00333

Therefore, the probability of receiving a defective part on the assembly line is approximately 0.00333 or 0.333%.