Question

Партия из 10 деталей содержит 4 бракованных. Найти вероятность, что из двух наугад взятых деталей будут 1 пригодна и 1 бракована. Партія з 10 деталей містить 4 браковані. Знайти ймовірність що з двох навмання взятих деталей будуть 1 придатна і 1 бракована.

Answer 1

Ответ:

$\frac{8}{15}$

Пошаговое объяснение:

Answer 2

To find the probability that out of two randomly selected parts, one will be usable and one will be defective, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total Number of Outcomes:

In this case, we have a batch of 10 parts, out of which 4 are defective. So, the total number of outcomes is the number of ways we can select 2 parts out of 10, which can be calculated using the combination formula:

Total Number of Outcomes = C(10, 2) = 10! / (2! * (10-2)!) = 45 [[1]].

Number of Favorable Outcomes:

To find the number of favorable outcomes, we need to consider the different ways we can select 1 usable part and 1 defective part from the batch.

1. Selecting 1 usable part: There are 6 usable parts in the batch (10 total parts - 4 defective parts). We can select 1 usable part in C(6, 1) = 6 ways. 2. Selecting 1 defective part: There are 4 defective parts in the batch. We can select 1 defective part in C(4, 1) = 4 ways.

Therefore, the number of favorable outcomes is the product of the number of ways to select 1 usable part and 1 defective part:

Number of Favorable Outcomes = C(6, 1) * C(4, 1) = 6 * 4 = 24.

Probability Calculation:

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:

Probability = Number of Favorable Outcomes / Total Number of Outcomes = 24 / 45 ≈ 0.5333.

Therefore, the probability that out of two randomly selected parts, one will be usable and one will be defective, is approximately 0.5333.

Please note that the calculations assume that the parts are selected without replacement, meaning that once a part is selected, it is not put back into the batch before the second part is selected.

I hope this helps! Let me know if you have any further questions.