Question

Бросают три игральные кости. Найти вероятность того, что 6 очков выпало не менее,чем двух костях.

Answer 1

Если бросают три кости, то всего вариантов, которые могут выпасть равняется 6^3=216

Нас устраивают только варианты:

6 6 6          6 6 5        6 6 4        6 6 3         6 6 2        6 6 1

6 5 6          6 4 6        6 3 6        6 2 6         6 1 6        5 6 6

4 6 6          3 6 6        2 6 6        1 6 6

Вероятность равна 16/216=0,074

Ответ: 0,074

Answer 2

Finding the Probability of Rolling at Least Two Sixes with Three Dice

To find the probability of rolling at least two sixes with three dice, we need to consider the different possible outcomes and calculate the probability for each outcome.

Let's break down the problem step by step:

1. Determine the total number of possible outcomes when rolling three dice. - When rolling one die, there are six possible outcomes (numbers 1 to 6). - Since we are rolling three dice, the total number of possible outcomes is 6 * 6 * 6 = 216.

2. Determine the number of favorable outcomes where at least two dice show a six. - To calculate this, we need to consider the different combinations of dice that can show a six. - There are three scenarios to consider: - Scenario 1: Two dice show a six, and the third die shows any number from 1 to 5. - Scenario 2: Two dice show a six, and the third die also shows a six. - Scenario 3: All three dice show a six.

3. Calculate the probability for each scenario. - Scenario 1: Two dice show a six, and the third die shows any number from 1 to 5. - The probability of rolling a six on a single die is 1/6. - The probability of rolling any number from 1 to 5 on a single die is 5/6. - Therefore, the probability for this scenario is (1/6) * (1/6) * (5/6) = 5/216.

- Scenario 2: Two dice show a six, and the third die also shows a six. - The probability of rolling a six on a single die is 1/6. - Therefore, the probability for this scenario is (1/6) * (1/6) * (1/6) = 1/216.

- Scenario 3: All three dice show a six. - The probability of rolling a six on a single die is 1/6. - Therefore, the probability for this scenario is (1/6) * (1/6) * (1/6) = 1/216.

4. Calculate the total probability by summing up the probabilities for each scenario. - Total probability = Probability of Scenario 1 + Probability of Scenario 2 + Probability of Scenario 3 - Total probability = (5/216) + (1/216) + (1/216) = 7/216.

Therefore, the probability of rolling at least two sixes with three dice is 7/216.

Please note that the probabilities calculated above are based on the assumption that the dice are fair and unbiased.