Question

В ящике имеются 15 деталей 5 из которых окрашены Наудачу дастают 5 деталей Найти вероятность того что 4 из них окрашены

Answer 1

$P= \frac{C_5^4\cdot C_{10}^1}{C_{15}^5} = \frac{5\cdot 10\; \cdot \; 5!}{15\cdot 14\cdot 13\cdot 12\cdot 11} \approx 0,01665$

Answer 2

Вариантов наличия в 5 выбранных деталях 4 окрашенных =
С из 5 по 4 умножить на С из 10 по 1 = 5*10=50, т.е. количество способов из 5 окрашеных выбрать 4 умножить на количество способов из 10 неокрашеных выбрать 1. Всего деталей 15, вариантов выбрать из них 5 = С из 15 по 5=15!/(5!*10!). Искомая вероятность=50/(15!/(5!10!))=
50*5!*10!/15!=50/3003

Answer 3

Problem Statement

You have a box with 15 parts, 5 of which are painted. You randomly select 5 parts from the box. What is the probability that 4 of them are painted?

Solution

To find the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.

# Total Number of Possible Outcomes

The total number of possible outcomes is the number of ways we can select 5 parts from the box, without considering whether they are painted or not. This can be calculated using the combination formula:

Total Number of Possible Outcomes = C(15, 5)

Where C(n, r) represents the number of combinations of n items taken r at a time.

# Number of Favorable Outcomes

The number of favorable outcomes is the number of ways we can select 4 painted parts and 1 non-painted part from the box. We can calculate this by multiplying the number of ways to select 4 painted parts from the 5 available painted parts, with the number of ways to select 1 non-painted part from the 10 remaining non-painted parts:

Number of Favorable Outcomes = C(5, 4) * C(10, 1)

# Probability

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

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

Let's calculate the probability:

Total Number of Possible Outcomes: Using the combination formula, we can calculate the total number of possible outcomes as follows: ``` Total Number of Possible Outcomes = C(15, 5) = 3003 ```

Number of Favorable Outcomes: Using the combination formula, we can calculate the number of favorable outcomes as follows: ``` Number of Favorable Outcomes = C(5, 4) * C(10, 1) = 5 * 10 = 50 ```

Probability: Now we can calculate the probability: ``` Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes = 50 / 3003 ≈ 0.0166 ```

Therefore, the probability that 4 out of the 5 randomly selected parts are painted is approximately 0.0166.

Please let me know if I can help you with anything else.