Question

Брат и сестра бросают игральную кость - каждый по одному разу. У кого выпадет меньше очков, тот моет посуду. Если выпадет поровну, то посуду моют вдвоем. С какой вероятностью посуду будет мыть брат в одиночку?

Answer 1

1/3 - вероятность того что посуду будет мыть брат в одиночку

Answer 2

Probability of the brother washing the dishes alone

To determine the probability of the brother washing the dishes alone, we need to consider the possible outcomes when rolling the dice. Since both the brother and sister roll the dice once each, there are a total of 36 possible outcomes (6 outcomes for the brother multiplied by 6 outcomes for the sister).

Let's analyze the possible outcomes:

- If the brother rolls a 1, there are 6 possible outcomes for the sister (1, 2, 3, 4, 5, 6). So, in this case, the brother will wash the dishes alone with a probability of 6/36. - If the brother rolls a 2, there are 5 possible outcomes for the sister (1, 2, 3, 4, 5). So, in this case, the brother will wash the dishes alone with a probability of 5/36. - Similarly, if the brother rolls a 3, there are 4 possible outcomes for the sister (1, 2, 3, 4). So, the probability of the brother washing the dishes alone is 4/36. - If the brother rolls a 4, there are 3 possible outcomes for the sister (1, 2, 3). So, the probability of the brother washing the dishes alone is 3/36. - If the brother rolls a 5, there are 2 possible outcomes for the sister (1, 2). So, the probability of the brother washing the dishes alone is 2/36. - If the brother rolls a 6, there is only 1 possible outcome for the sister (1). So, the probability of the brother washing the dishes alone is 1/36.

To find the total probability of the brother washing the dishes alone, we sum up the probabilities for each possible outcome:

(6/36) + (5/36) + (4/36) + (3/36) + (2/36) + (1/36) = 21/36

Therefore, the probability of the brother washing the dishes alone is 21/36.

Please note that the search results provided by You.com did not directly answer the question. The calculation of probabilities was done based on the rules provided in the question.