Question

В ящике лежат шары:5 красных,7 синих,1 зелёный.Сколько шаров надо вынуть,чтобы достать 2 шара одного цвета? Варианты ответа: А-2 Б-5 В-7 Г-11

Answer 1

Б-5 ..........................:-) :-) :-) :-) :-) :-) :-) :-)

Answer 2

Ну вообще 4, но так как тут нету этого варианта ответа, то Б-5

Answer 3

Question Analysis

The question asks how many balls need to be drawn in order to obtain 2 balls of the same color from a box containing 5 red balls, 7 blue balls, and 1 green ball. The options for the answer are A) 2, B) 5, C) 7, and D) 11.

Answer

To determine the minimum number of balls that need to be drawn to obtain 2 balls of the same color, we can use the concept of the pigeonhole principle. The pigeonhole principle states that if you have more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. In this case, the pigeons are the balls and the pigeonholes are the colors.

Since there are 5 red balls, 7 blue balls, and 1 green ball, there are a total of 13 balls. To guarantee that we have at least 2 balls of the same color, we would need to draw 13 + 1 = 14 balls. This is because if we draw 13 balls, we could have 1 ball of each color, and the next ball we draw would guarantee that we have at least 2 balls of the same color.

Therefore, the correct answer is not among the options provided. The correct answer is 14.

Explanation

The pigeonhole principle is a mathematical principle that states that if you have more objects than you have containers to put them in, then at least one container must contain more than one object. In this case, the objects are the balls and the containers are the colors.

To apply the pigeonhole principle, we need to consider the worst-case scenario, which is that we draw one ball of each color before drawing a ball of the same color. In this scenario, we would need to draw all 5 red balls, all 7 blue balls, and the green ball before we have 2 balls of the same color. This gives us a total of 5 + 7 + 1 = 13 balls.

However, to guarantee that we have at least 2 balls of the same color, we would need to draw one more ball. This is because if we draw 13 balls, we could have 1 ball of each color, and the next ball we draw would guarantee that we have at least 2 balls of the same color.

Therefore, we would need to draw a total of 13 + 1 = 14 balls to obtain 2 balls of the same color.

Example

Let's consider an example to illustrate this. Suppose we draw the balls in the following order: red, blue, green, red, blue, red, blue, red, blue, red, blue, red, blue, red. In this case, we would need to draw 14 balls to obtain 2 balls of the same color (red in this case).

Conclusion

To obtain 2 balls of the same color from a box containing 5 red balls, 7 blue balls, and 1 green ball, we would need to draw a total of 14 balls.