Question

Юля бросает игральный кубик. В сумме у нее выпало 6 очков. Найдите вероятность того, что при первом броске выпало 2 очка.

Answer 1

По формуле Байеса: $P(B_6/A)= \dfrac{P(A/B_6)P(B_6)}{\sum^5_{i=2}P(A/B_i)P(B_{6-i})}$

где $B_i$ на I кубике  не выпало очко 2 и A - выпадение двух костей в сумме которых даст 6

$P(B_6/A)= \dfrac{ \frac{1}{6} \cdot\frac{1}{6}}{\frac{1}{6}\cdot\frac{1}{6}+\frac{1}{6}\cdot\frac{1}{6}+\frac{1}{6}\cdot\frac{1}{6}+\frac{1}{6}\cdot\frac{1}{6}+\frac{1}{6}\cdot\frac{1}{6}} =\dfrac{1}{5}$

ВТОРОЙ СПОСОБ. Все возможные варианты : {2;4}, {1;5}, {5;1}, {4;2} , {3;3}
При первом броске выпало 2 очка и из возможных вариантов благоприятствующих ему 1

Искомая вероятность, по определению: P = 1/5

Answer 2

Calculating the Probability of Rolling a 2 on the First Throw

To calculate the probability of rolling a 2 on the first throw, we need to know the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes when rolling a standard six-sided die is 6, as there are six faces on the die numbered from 1 to 6.

To find the number of favorable outcomes, we need to know the sum of the numbers rolled by the die. In this case, the sum of the numbers rolled by the die is 6.

Now, we need to determine the number of ways we can obtain a sum of 6 using two dice. We can do this by listing all the possible combinations:

- 1 + 5 - 2 + 4 - 3 + 3 - 4 + 2 - 5 + 1

From the above combinations, we can see that there is only one combination that results in a sum of 6, which is 1 + 5.

Therefore, the number of favorable outcomes is 1.

Now, we can calculate the probability of rolling a 2 on the first throw by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

Probability = 1 / 6

So, the probability of rolling a 2 on the first throw is 1/6.

Please note that the above calculation assumes a fair six-sided die and that each face has an equal chance of landing face-up.