Question

В коробке по паре коричневых и черных носков.Сколько нужно взять носков,Не глядя,чтобы получилась одна пара

Answer 1

Ответ: 3, потому что надо рассматривать неудачный случай.
у нас 4 носка (2 коричневых, 2 чёрных) надо вытащить пару носков 1 цвета
рассматриваем только неудачный случай:
берём первый раз - чёрный носок
берём второй раз - коричневый носок 
берём третий раз - не важно чёрный или коричневый. У нас есть пара.

Answer 2

Calculating the Number of Socks

To calculate the number of socks needed to ensure at least one pair of matching socks without looking, we can use the concept of probability.

Probability Calculation: The probability of getting a pair of socks without looking can be calculated using the formula: $$ P=\frac{C_{n}^2}{C_{N}^2} $$ Where: - $C_{n}^2$ represents the number of ways to choose 2 socks from the same color. - $C_{N}^2$ represents the total number of ways to choose 2 socks from the entire set of socks.

Applying the Formula

Using the provided formula, we can calculate the number of socks needed to ensure at least one pair without looking.

Calculation Example: Let's assume there are 10 socks in the box, with a mix of brown and black socks. We want to find out how many socks need to be taken without looking to ensure at least one pair.

The formula can be applied as follows: $$ P=\frac{C_{5}^2 \cdot C_{5}^{0}}{C_{10}^2} = \frac{10 \cdot 1}{45} = \frac{2}{9} = 0.222 $$

Conclusion

Based on the calculation, to ensure at least one pair of matching socks without looking, approximately 4 socks need to be taken from the box.

This calculation ensures a high probability of obtaining a matching pair of socks without the need to look at the socks.