Question

В партии из 15 деталей имеется 3 стандартных. Наудачу отобраны 4 детали. Найти вероятность того, что среди отобранных деталей ровно 2 стандартных.

Answer 1

Problem Statement

В партии из 15 деталей имеется 3 стандартных. Наудачу отобраны 4 детали. Найти вероятность того, что среди отобранных деталей ровно 2 стандартных.

Solution

To find the probability of selecting exactly 2 standard parts out of 4 randomly selected parts, we can use the concept of combinations.

The total number of ways to select 4 parts out of 15 is given by the combination formula:

C(n, r) = n! / (r!(n-r)!)

Where n is the total number of parts (15 in this case) and r is the number of parts to be selected (4 in this case).

The number of ways to select 2 standard parts out of 3 is given by the combination formula:

C(3, 2) = 3! / (2!(3-2)!) = 3

The number of ways to select the remaining 2 non-standard parts out of 12 is given by the combination formula:

C(12, 2) = 12! / (2!(12-2)!) = 66

Therefore, the total number of ways to select exactly 2 standard parts out of 4 is given by:

C(3, 2) * C(12, 2) = 3 * 66 = 198

The total number of ways to select 4 parts out of 15 is given by:

C(15, 4) = 15! / (4!(15-4)!) = 1365

Therefore, the probability of selecting exactly 2 standard parts out of 4 is:

P = (number of ways to select exactly 2 standard parts out of 4) / (total number of ways to select 4 parts out of 15) = 198 / 1365 ≈ 0.1453

So, the probability of selecting exactly 2 standard parts out of 4 randomly selected parts is approximately 0.1453.