Question

Игральную кость бросают дважды.найдите вероятность того, что в сумме выпадет 3 или 6 или 12 очков

Answer 1

1 + 1 = 2

1 + 4 = 5

2 + 3 = 5

3 + 2 = 5

4 + 1 = 5

4 + 6 = 10

6 + 4 = 10

5 + 5 = 10

Итак, благоприятных исходов - 8.

Вариантов выпадения очков на первой и второй игральной кости - по 6, т.е. всего 6 * 6 = 36.

Искомая вероятность равна:

Р=8:36=2:9

Answer 2

To find the probability of rolling a total of 3, 6, or 12 on two dice, we'll first calculate the possible combinations that result in these sums and then determine the total number of possible outcomes when rolling two dice.

When rolling two dice, each die has 6 sides with values ranging from 1 to 6. To calculate the probability, we'll create a table of all possible outcomes:

Die 1	Die 2	Sum
1	1	2
1	2	3
1	3	4
1	4	5
1	5	6
1	6	7
2	1	3
2	2	4
2	3	5
2	4	6
2	5	7
2	6	8
3	1	4
3	2	5
3	3	6
3	4	7
3	5	8
3	6	9
4	1	5
4	2	6
4	3	7
4	4	8
4	5	9
4	6	10
5	1	6
5	2	7
5	3	8
5	4	9
5	5	10
5	6	11
6	1	7
6	2	8
6	3	9
6	4	10
6	5	11
6	6	12

Now, we count the number of favorable outcomes for the sums 3, 6, and 12:

• Sum of 3: There is only one way to get a sum of 3 (1+2).
• Sum of 6: There are two ways to get a sum of 6 (1+5 and 2+4).
• Sum of 12: There is only one way to get a sum of 12 (6+6).

Now, we calculate the total number of possible outcomes when rolling two dice, which is 6 (number of sides on one die) * 6 (number of sides on the other die) = 36.

Finally, we find the probability:

Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes) Probability = (1 + 2 + 1) / 36 Probability = 4 / 36 Probability = 1 / 9

So, the probability of getting a total of 3, 6, or 12 when rolling two dice is 1/9.