Question

В случайном эксперементе бросают три игральные кости . найти вероятность того, что сумма выпавших очков равна 6. Результат округлите до тысячных. ( вообще объясните как такие задачи делать?)

Answer 1

При трёх бросках кубика всего 6³ = 216 вариантов выпадения очков.
6 очков может выпасть в следующих случаях
114
123
132
141
213
222
231
312
321
411
Всего 10 вариантов.
Считаем вероятность:
$\frac{10}{216} \approx 0,046$

Answer 2

Solving the Probability Problem of Rolling Three Dice

To find the probability of the sum of the numbers on three dice being equal to 6, we can break down the problem into smaller steps.

Step 1: Determine the Total Number of Outcomes When rolling three dice, each die has 6 possible outcomes (1, 2, 3, 4, 5, 6). Therefore, the total number of outcomes when rolling three dice is 6 * 6 * 6 = 216.

Step 2: Identify the Favorable Outcomes We need to find the combinations of numbers on the three dice that sum up to 6. These combinations include (1, 1, 4), (1, 2, 3), (1, 3, 2), (1, 4, 1), (2, 1, 3), (2, 2, 2), (2, 3, 1), (3, 1, 2), (3, 2, 1), and (4, 1, 1).

Step 3: Calculate the Probability The probability of an event is given by the formula: \[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]

Now, let's calculate the probability.

Calculating the Probability

The number of favorable outcomes is 10 (as identified in Step 2), and the total number of outcomes is 216 (as calculated in Step 1).

\[ \text{Probability} = \frac{10}{216} \]

\[ \text{Probability} \approx 0.046 \]

Therefore, the probability of the sum of the numbers on three dice being equal to 6 is approximately 0.046.

This approach breaks down the problem into manageable steps, making it easier to calculate the probability of a specific outcome in a random experiment involving multiple events.