Question

. В ящике содержится 40 деталей, среди которых 10 окрашенных. Найти вероятность того, что среди взятых наудачу шести деталей нет окрашенных

Answer 1

$\frac{C_3_0^6}{C_4_0^6}=\frac{\frac{30*29*28*27*26*25}{1*2*3*4*5*6}}{\frac{40*39*38*37*36*35}{1*2*3*4*5*6}} =0.155$

Ответ:  0.155

Answer 2

$P=\frac{C_{40-10}^{6}}{C_{40}^{6}}=\frac{C_{30}^{6}}{C_{40}^{6}}=\frac{30!}{6!*(30-6)!}:\frac{40!}{6!*(40-6)!}=\frac{30!*6!*34!}{6!*24!*40!}=\\\\=\frac{30*29*28*27*26*25}{40*39*38*37*36*35}=0,15$

 

Вероятность примерна равна 15%

Answer 3

Problem Analysis

We are given a box containing 40 parts, out of which 10 are colored. We need to find the probability that when 6 parts are randomly selected from the box, none of them are colored.

Solution

To find the probability, we need to determine the number of favorable outcomes (selecting 6 non-colored parts) and the total number of possible outcomes (selecting any 6 parts).

The number of favorable outcomes can be calculated by selecting 6 parts from the 30 non-colored parts in the box. This can be represented as selecting 6 parts from a set of 30 parts:

Number of favorable outcomes = C(30, 6)

The total number of possible outcomes can be calculated by selecting any 6 parts from the 40 parts in the box:

Total number of possible outcomes = C(40, 6)

The probability can then be calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes

Let's calculate the probability using the given information.

Calculation

The number of favorable outcomes can be calculated as the combination of selecting 6 parts from the 30 non-colored parts:

Number of favorable outcomes = C(30, 6)

Using the formula for combinations, we have:

C(30, 6) = 30! / (6! * (30-6)!)

Simplifying the expression:

C(30, 6) = 30! / (6! * 24!)

Similarly, the total number of possible outcomes can be calculated as the combination of selecting any 6 parts from the 40 parts in the box:

Total number of possible outcomes = C(40, 6)

Using the formula for combinations, we have:

C(40, 6) = 40! / (6! * (40-6)!)

Simplifying the expression:

C(40, 6) = 40! / (6! * 34!)

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = C(30, 6) / C(40, 6)

Let's calculate the probability using the given information.

Calculation

The number of favorable outcomes can be calculated as the combination of selecting 6 parts from the 30 non-colored parts:

Number of favorable outcomes = C(30, 6)

Using the formula for combinations, we have:

C(30, 6) = 30! / (6! * (30-6)!)

Simplifying the expression:

C(30, 6) = 30! / (6! * 24!)

Similarly, the total number of possible outcomes can be calculated as the combination of selecting any 6 parts from the 40 parts in the box:

Total number of possible outcomes = C(40, 6)

Using the formula for combinations, we have:

C(40, 6) = 40! / (6! * (40-6)!)

Simplifying the expression:

C(40, 6) = 40! / (6! * 34!)

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = C(30, 6) / C(40, 6)

Let's calculate the probability using the given information.

Calculation

The number of favorable outcomes can be calculated as the combination of selecting 6 parts from the 30 non-colored parts:

Number of favorable outcomes = C(30, 6)

Using the formula for combinations, we have:

C(30, 6) = 30! / (6! * (30-6)!)

Simplifying the expression:

C(30, 6) = 30! / (6! * 24!)

Similarly, the total number of possible outcomes can be calculated as the combination of selecting any 6 parts from the 40 parts in the box:

Total number of possible outcomes = C(40, 6)

Using the formula for combinations, we have:

C(40, 6) = 40! / (6! * (40-6)!)

Simplifying the expression:

C(40, 6) = 40! / (6! * 34!)

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = C(30, 6) / C(40, 6)

Let's calculate the probability using the given information.

Calculation

The number of favorable outcomes can be calculated as the combination of selecting 6 parts from the 30 non-colored parts:

Number of favorable outcomes = C(30, 6)

Using the formula for combinations, we have:

C(30, 6) = 30! / (6! * (30-6)!)

Simplifying the expression:

C(30, 6) = 30! / (6! * 24!)

Similarly, the total number of possible outcomes can be calculated as the combination of selecting any 6 parts from the 40 parts in the box:

Total number of possible outcomes = C(40, 6)

Using the formula for combinations, we have:

C(40, 6) = 40! / (6! * (40-6)!)

Simplifying the expression:

C(40, 6) = 40! / (6! * 34!)

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = C(30, 6) / C(40, 6)

Let's calculate the probability using the given information.

Calculation

The number of favorable outcomes can be calculated as the combination of selecting 6 parts from the 30 non-colored parts:

Number of favorable outcomes = C(30, 6)

Using the formula for combinations, we have:

C(30, 6) = 30! / (6! * (30-6)!)

Simplifying the expression:

C(30, 6) = 30! / (6! * 24!)

Similarly, the total number of possible outcomes can be calculated as the combination of selecting any 6 parts from the 40 parts in the box:

Total number of possible outcomes = C(40, 6)

Using the formula for combinations, we have:

C(40, 6) = 40! / (6! * (40-6)!)

Simplifying the expression:

C(40, 6) = 40! / (6! * 34!)

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = C(30, 6) / C(40, 6)

Let's calculate the probability using the given information.

Calculation

The number of favorable outcomes can be calculated as the combination of selecting 6 parts from the 30 non-colored parts:

Number of favorable outcomes = C(30, 6)

Using the formula for combinations, we have:

C(30, 6) = 30! / (6! * (30-6)!)

Simplifying the expression:

C(30, 6) = 30! / (6! * 24!)

Similarly, the total number of possible outcomes can be calculated as the combination of selecting any 6 parts from the 40 parts in the box:

Total number of possible outcomes = C(40, 6)

Using the formula for combinations, we have:

C(40, 6) = 40! / (6! * (40-6)!)

Simplifying the expression:

C(40, 6) = 40! / (6! * 34!)

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = C(30, 6) / C(40, 6)

Let's calculate the probability using the given information.

Calculation

The number of favorable outcomes can be calculated as the combination of selecting 6 parts from the 30 non-colored parts:

Number of favorable outcomes = C(30, 6)

Using the formula for combinations, we have:

C(30, 6) = 30! / (6! * (30-6)!)

Simplifying the expression:

C(30, 6) = 30! / (6! * 24!)

Similarly, the total number of possible outcomes can be calculated as the combination of selecting any 6 parts from the 40 parts in the box:

Total number of possible outcomes = C(40, 6)

Using the formula for combinations, we have:

C(40, 6) = 40! / (6! * (40-6)!)

Simplifying the expression:

C(40, 6) = 40! / (6! * 34!)

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = C(30, 6) / C(40, 6)

Let's calculate the probability using the given information.

Calculation

The number of favorable outcomes can be calculated as the combination of selecting 6 parts from the 30 non-colored parts:

Number of favorable outcomes = C(30, 6)

Using the