Question

в урне находится 3 желтых, 4 зеленых и 5 красных шаров. из урны наудачу вынули 3 шара. какова вероятность того, что они разного цвета

Answer 1

Решение .

  Всего шаров будет 3+4+5=12 .

Применяем формулу классической вероятности   $P=\dfrac{m}{n}$    .

Вероятность того, что достали шары разного цвета, равна

$P=\dfrac{C_3^1\cdot C_4^1\cdot C_5^1}{C_{12}^3}=\dfrac{3\cdot 4\cdot 5}{\dfrac{12\cdot 11\cdot 10}{3!}}=\dfrac{3!}{11\cdot 2}=\dfrac{3}{11}\approx \boldsymbol{0,2727}$              

Answer 2

Calculating the Probability of Drawing Three Balls of Different Colors

To calculate the probability of drawing three balls of different colors from the urn, we can use the concept of combinations. The total number of ways to draw 3 balls from 12 (3 yellow, 4 green, and 5 red) is given by the combination formula:

Total number of ways to draw 3 balls from 12: ``` C(12, 3) = 12! / (3!(12-3)!) = 220 ```

Next, we calculate the number of ways to draw 3 balls of different colors. We can do this by calculating the number of ways to choose one ball of each color:

Number of ways to draw 3 balls of different colors: ``` Ways to choose 1 yellow, 1 green, and 1 red ball = C(3, 1) * C(4, 1) * C(5, 1) = 3 * 4 * 5 = 60 ```

Calculating the Probability

Now, we can calculate the probability of drawing three balls of different colors by dividing the number of favorable outcomes by the total number of outcomes:

Probability of drawing three balls of different colors: ``` Probability = Number of ways to draw 3 balls of different colors / Total number of ways to draw 3 balls = 60 / 220 = 3 / 11 ```

So, the probability of drawing three balls of different colors from the urn is 3/11.