Question

Помогите, пожалуйста,очень надо.брак в продукции завода вследствие дефекта А составляет 5%, причем среди забракованной по признаку А продукции в 10% случаев встречается дефект Е, а в продукции, свободной от дефекта А, дефект Е встречается 1% случаев. Найти вероятность встречи дефекта Е во всей продукции.

Answer 1

Типо так
0,5*0,1+0,95*0,01=0,0145

Answer 2

Calculation of the Probability of Defect E in the Entire Production

To calculate the probability of encountering defect E in the entire production, we need to consider the probability of encountering defect E in the defective products and the probability of encountering defect E in the products without defect A.

Let's denote the probability of encountering defect E in the defective products as P(E|A) and the probability of encountering defect E in the products without defect A as P(E|~A).

Given the information provided, we have the following probabilities:

- The defect rate due to defect A is 5% (0.05). - Among the defective products (with defect A), defect E occurs in 10% (0.10) of the cases. - Among the products without defect A, defect E occurs in 1% (0.01) of the cases.

To calculate the probability of encountering defect E in the entire production, we can use the law of total probability:

P(E) = P(E|A) * P(A) + P(E|~A) * P(~A)

where P(A) is the probability of encountering defect A, and P(~A) is the probability of encountering a product without defect A.

Let's substitute the values into the formula:

P(E) = 0.10 * 0.05 + 0.01 * (1 - 0.05)

Simplifying the equation:

P(E) = 0.005 + 0.01 * 0.95

Calculating the result:

P(E) = 0.005 + 0.0095 = 0.0145

Therefore, the probability of encountering defect E in the entire production is 0.0145 or 1.45%.

Please note that the above calculation is based on the information provided and assumes independence between the occurrence of defect A and defect E.