Question

На фабрике керамической посуды 10% произведённых тарелок имеют дефект. При контроле качества продукции выявляется 80% дефектных тарелок. Остальные тарелки поступают в продажу. Найдите вероятность того, что случайно выбранная при по­купке тарелка не имеет дефектов. Результат округлите до сотых.только норм объясните:3

Answer 1

Вероятность - это отношение числа благоприятных исходов к общему числу исходов. Общее число исходов - это всё количество тарелок = х
Найдём с дефектом  10%  с дефектом ( это 0,1 х), но при контроле качества  выявляются только 80% ( 0,1 х - 100%
                                            ?     - 80%)
80 · 0,1 х: 100 = 0,08 х - это тарелки с дефектом,   
В продажу поступает не х тарелок, а  х - 0,08 х = 0,92 х
Их х тарелок без дефекта 0,9 х
Р(А) = 0,9 х: 0,92 х ≈ 0,98

Answer 2

Calculation of the Probability

To find the probability that a randomly chosen plate does not have any defects, we need to consider the information provided:

- 10% of the plates produced have defects. - During quality control, 80% of the defective plates are identified, while the rest are sold.

To calculate the probability, we can use the following formula:

P(plate without defects) = 1 - P(plate with defects)

Let's calculate the probability step by step:

1. Calculate the probability of a plate having defects: - 10% of the plates produced have defects. - Therefore, the probability of a plate having defects is 0.1.

2. Calculate the probability of a plate being identified as defective during quality control: - 80% of the defective plates are identified during quality control. - Therefore, the probability of a plate being identified as defective is 0.8.

3. Calculate the probability of a plate not being identified as defective during quality control: - The remaining 20% of the defective plates are not identified during quality control. - Therefore, the probability of a plate not being identified as defective is 0.2.

4. Calculate the probability of a plate not having defects: - P(plate without defects) = 1 - P(plate with defects) - P(plate without defects) = 1 - (probability of a plate being identified as defective during quality control) - P(plate without defects) = 1 - 0.8 - P(plate without defects) = 0.2

Therefore, the probability that a randomly chosen plate does not have any defects is 0.2 or 20% (rounded to the nearest hundredth).

Please let me know if you need any further clarification or assistance!