Question

Игральный кубик бросают 2 раза. С какой вероятностью выпавшие числа будут отличаться на 3? Ответ округлить до сотых.Помогите, желательно с объяснением, а не просто ответ.

Answer 1

Число комбинаций 36;
Где выпавшие числа будут отличаться на 3 только в 6 случаях:
1-4
2-5
3-6
4-1
5-2
6-3
Значит, вероятность будет = 6/36=1/6=0,17.
Ответ: вероятность того что числа будут отличатся на 3 равна 0,17.

Answer 2

Probability of Dice Rolls Differing by 3

To calculate the probability of the numbers on two dice differing by 3, we can first determine the total number of outcomes when rolling two dice and then find the number of favorable outcomes where the numbers differ by 3.

Let's break it down step by step:

1. Total Number of Outcomes when Rolling Two Dice: - When rolling two dice, each die has 6 possible outcomes (1, 2, 3, 4, 5, 6). - Therefore, the total number of outcomes when rolling two dice is 6 * 6 = 36.

2. Favorable Outcomes where the Numbers Differ by 3: - To find the favorable outcomes, we can consider the pairs of numbers on the two dice that differ by 3. - These pairs can be (1, 4), (2, 5), (3, 6), (4, 1), (5, 2), and (6, 3). - So, there are 6 favorable outcomes where the numbers differ by 3.

3. Calculating the Probability: - The probability of an event is given by the formula: \[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \] - Substituting the values, we get: \[ \text{Probability} = \frac{6}{36} = \frac{1}{6} \]

Therefore, the probability of the numbers on two dice differing by 3 is 1/6, which is approximately 0.17 when rounded to the nearest hundredth.