Question

Игральный кубик бросают дважды. Известно, что хотя бы раз выпало 2. Найдите вероятность того, что в сумме выпадет не меньше чем 5.

Answer 1

Ответ:

Вероятность равна 2/3

Объяснение:

Чтоб вышла сумма больше или равная пяти, должно выпасть 3,4,5 или 6 (четыре варианта). На игральной кости 6 чисел. Вероятность равна количеству удачных исходов ÷ на количество всех исходов.

4/6, сокращаем = 2/3

Answer 2

Problem Analysis

We are given that a fair six-sided die is rolled twice. We know that at least once a 2 is rolled. We need to find the probability that the sum of the two rolls is at least 5.

Solution

To find the probability, we need to determine the total number of favorable outcomes and the total number of possible outcomes.

Let's consider the possible outcomes when rolling the die twice: - The first roll can be any number from 1 to 6. - The second roll can also be any number from 1 to 6.

To find the total number of possible outcomes, we multiply the number of possibilities for each roll: 6 * 6 = 36.

Now let's consider the favorable outcomes, i.e., the outcomes where the sum of the two rolls is at least 5. We can calculate these outcomes by listing all the possible combinations:

- The sum of 5 can be obtained in the following ways: (1, 4), (2, 3), (3, 2), (4, 1). - The sum of 6 can be obtained in the following ways: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1). - The sum of 7 can be obtained in the following ways: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). - The sum of 8 can be obtained in the following ways: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2). - The sum of 9 can be obtained in the following ways: (3, 6), (4, 5), (5, 4), (6, 3). - The sum of 10 can be obtained in the following ways: (4, 6), (5, 5), (6, 4). - The sum of 11 can be obtained in the following ways: (5, 6), (6, 5). - The sum of 12 can be obtained in the following way: (6, 6).

Counting these favorable outcomes, we find that there are 30 possible outcomes where the sum of the two rolls is at least 5.

Therefore, the probability that the sum of the two rolls is at least 5 is given by the ratio of the number of favorable outcomes to the number of possible outcomes:

Probability = Number of Favorable Outcomes / Number of Possible Outcomes

Probability = 30 / 36

Simplifying the fraction, we get:

Probability = 5 / 6

So, the probability that the sum of the two rolls is at least 5 is 5/6.

Answer

The probability that the sum of the two rolls is at least 5 is 5/6.