Question

. Брак при производстве изделия вследствие дефекта A составляет 6%, вследствие дефекта B 7%. Процент годной продукции составляет 90%. Найти вероятность, что наудачу взятое изделие имеет только дефект A.

Answer 1

Вероятность, что изделие имеет дефект А p(A) = 0,06.
Вероятность, что изделие имеет дефект В p(B) = 0,07.
Вероятность, что изделие имеет дефект А или дефект В,
p(AUB) = 0,1 (то есть 10%, т.к. процент годной продукции по условию 90%)
p(AUB) = p(A) + p(B) - p(A∩B),
где p(A∩B) - это вероятность, что изделие имеет и дефект А, и дефект В.
Тогда (выражая p(A∩B) из предыдущего равенства) 
p(A∩B) = p(A)+p(B) - p(AUB) = 0,06 + 0,07 - 0,1 = 0,13 - 0,1 = 0,03.
Искомая вероятность, это вероятность, что изделие имеет только дефект А и при этом не имеет дефекта В, то есть искомая вероятность это p(A - A∩B) = p(A) - p(A∩B) = 0,06 - 0,03 = 0,03.
Ответ. 0,03.

Answer 2

Calculation of the Probability

To find the probability that a randomly selected item has only defect A, we can use the given information. Let's break down the problem step by step:

1. The probability of a defect A is given as 6% or 0.06. 2. The probability of a defect B is given as 7% or 0.07. 3. The percentage of good products is given as 90% or 0.90.

To calculate the probability that a randomly selected item has only defect A, we need to consider two scenarios: 1. The item has only defect A and is not defective in any other way. 2. The item has defect A along with defect B or other defects.

Let's calculate the probability for each scenario:

Scenario 1: The item has only defect A and is not defective in any other way.

To calculate the probability for this scenario, we need to consider the following: 1. The probability of having only defect A is 0.06. 2. The probability of not having defect B is 1 - 0.07 = 0.93. 3. The probability of not having any other defects is 0.90.

To find the probability of this scenario, we multiply these probabilities together:

Probability of having only defect A = 0.06 * 0.93 * 0.90 = 0.05022

Therefore, the probability that a randomly selected item has only defect A is approximately 0.05022 or 5.022%.

Scenario 2: The item has defect A along with defect B or other defects.

To calculate the probability for this scenario, we need to consider the following: 1. The probability of having defect A is 0.06. 2. The probability of having defect B is 0.07. 3. The probability of having other defects is 1 - 0.90 = 0.10.

To find the probability of this scenario, we multiply these probabilities together:

Probability of having defect A along with defect B or other defects = 0.06 * 0.07 * 0.10 = 0.00042

Therefore, the probability that a randomly selected item has defect A along with defect B or other defects is approximately 0.00042 or 0.042%.

Final Answer:

To find the probability that a randomly selected item has only defect A, we add the probabilities from both scenarios:

Probability of having only defect A = 0.05022 + 0.00042 = 0.05064

Therefore, the probability that a randomly selected item has only defect A is approximately 0.05064 or 5.064%.

Please note that these calculations are based on the given information and assumptions made.