Question

В партії із 10 деталей 8 стандартних. Знайдіть імовірність того, що серед навмання вибраних 2 деталей вони будуть стандартними.

Answer 1

Выбираем две детали из 8 стандартных.

Вероятность равна 2/8=1/4=0,25

Answer 2

Calculating the Probability of Selecting 2 Standard Parts from a Set of 10

To calculate the probability of randomly selecting 2 standard parts from a set of 10, we can use the formula for calculating combinations. The formula for combinations is:

nCr = n! / (r! * (n-r)!)

Where: - n is the total number of items in the set - r is the number of items to be chosen - ! denotes factorial, which means the product of all positive integers up to that number

Applying the Formula

In this case, we have: - n = 10 (total number of parts) - r = 2 (number of parts to be chosen)

Using the formula, we can calculate the number of ways to choose 2 standard parts from 10.

10C2 = 10! / (2! * (10-2)!)

Let's calculate this to find the total number of ways to choose 2 standard parts from 10.

Calculation

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

2! = 2 × 1 = 2

8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320

Now, let's substitute these values into the formula and calculate the result.

10C2 = 3,628,800 / (2 × 40,320) = 45

Probability Calculation

Now that we know there are 45 ways to choose 2 standard parts from 10, we can calculate the probability.

The probability of choosing 2 standard parts from 10 can be calculated using the formula:

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

In this case, the number of favorable outcomes is 45 (as calculated above), and the total number of possible outcomes is the total number of ways to choose 2 parts from 10, which is also 45.

So, the probability is:

Probability = 45 / 45 = 1

Therefore, the probability of randomly selecting 2 standard parts from a set of 10 and having them both be standard parts is 1 or 100%.