Question

В ящике 16 серых носков и 12 черных. Папа не глядя вытащил из ящика 3 носка. Какова вероятность, что среди них ровно 2 черных?

Answer 1

Ответ:

0,07 или 7%

Пошаговое объяснение:

P(a) = m/n

m - количество благоприятных событий ( в нашем случае 2)

n - общее количество событий ( у нас 28 )

2/28 = 0.07

Я не знаю как вы записываете вероятность, но можешь записать просто число, или 7%, если записываете в процентах

Answer 2

Problem Analysis

To find the probability of drawing exactly 2 black socks out of 3 socks from a box containing 16 gray socks and 12 black socks, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

Total Number of Outcomes

The total number of outcomes is the number of ways we can choose 3 socks from a total of 28 socks (16 gray socks + 12 black socks). This can be calculated using the combination formula:

Total Number of Outcomes = C(28, 3)

Number of Favorable Outcomes

The number of favorable outcomes is the number of ways we can choose 2 black socks and 1 gray sock from a total of 28 socks. This can be calculated using the combination formula:

Number of Favorable Outcomes = C(12, 2) * C(16, 1)

Probability Calculation

The probability of drawing exactly 2 black socks out of 3 socks can be calculated by dividing the number of favorable outcomes by the total number of outcomes:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

Let's calculate the probability.

Calculation

Using the combination formula, we can calculate the total number of outcomes and the number of favorable outcomes:

Total Number of Outcomes = C(28, 3) = 28! / (3! * (28-3)!) = 3276

Number of Favorable Outcomes = C(12, 2) * C(16, 1) = (12! / (2! * (12-2)!) * (16! / (1! * (16-1)!)) = 792 * 16 = 12672

Now, we can calculate the probability:

Probability = Number of Favorable Outcomes / Total Number of Outcomes = 12672 / 3276 ≈ 3.87

Therefore, the probability of drawing exactly 2 black socks out of 3 socks is approximately 3.87%.