Question

) В партии из 10 деталей имеется 8 стандартных. Найдите вероятность того, что среди 7 взятых наугад деталей ровно 5 стандартных.

Answer 1

Problem Statement

We are given a set of 10 parts, out of which 8 are standard. We need to find the probability that out of 7 randomly selected parts, exactly 5 are standard.

Solution

To solve this problem, we can use the concept of combinations. The probability of selecting exactly 5 standard parts out of 7 can be calculated using the formula:

P = (number of ways to choose 5 standard parts) / (total number of ways to choose 7 parts)

Let's calculate each part of the formula step by step.

1. Number of ways to choose 5 standard parts: - We have 8 standard parts in total. - We need to choose 5 out of these 8 parts. - The number of ways to choose 5 parts out of 8 can be calculated using the combination formula: C(8, 5).

2. Total number of ways to choose 7 parts: - We have a total of 10 parts. - We need to choose 7 out of these 10 parts. - The number of ways to choose 7 parts out of 10 can be calculated using the combination formula: C(10, 7).

3. Calculating the probability: - We divide the number of ways to choose 5 standard parts by the total number of ways to choose 7 parts. - The probability can be calculated as: P = C(8, 5) / C(10, 7).

Let's calculate the probability using the given formula.

Calculation

Using the combination formula, we can calculate the number of ways to choose 5 standard parts and the total number of ways to choose 7 parts.

- Number of ways to choose 5 standard parts: C(8, 5) = 56 - Total number of ways to choose 7 parts: C(10, 7) = 120

Now, we can calculate the probability:

P = 56 / 120 = 0.4667

Therefore, the probability that exactly 5 out of 7 randomly selected parts are standard is approximately 0.4667.

Answer

The probability that exactly 5 out of 7 randomly selected parts are standard is approximately 0.4667.