Question

Помогите пожалуйста!! Найдите вероятность того что случайно выбранное трёхзначное число будет делиться на 11

Answer 1

Вероятность - это отношение числа благоприятных исходов к общему числу исходов.
Благоприятные исходы - это все трёхзначные числа, кратные 11
Общее число исходов - это количество всех трёхзначных чисел.
Числа, которые делятся на 11:
110, 121, 132, 143, 154, 165, 176, 187,  198, 209
220, 231, 242, 253, 264, 275, 286,  297, 308, 319,
330, 341, 352,  363, 374, 385, 396, 407, 418, 429,
440, ...
Всего таких чисел 9*9 = 81
Всего трёхзначных чисел 900
Р(А) = 81/900= 0,09= 9%

Answer 2

Calculating the Probability of a Three-Digit Number Being Divisible by 11

To find the probability of a randomly chosen three-digit number being divisible by 11, we can use the following approach:

1. Total Possible Three-Digit Numbers: - The total number of three-digit numbers can be calculated using the formula: \(9 \times 10 \times 10 = 900\). This is because the first digit cannot be zero, and the second and third digits can be any number from 0 to 9.

2. Counting the Numbers Divisible by 11: - We need to find the count of three-digit numbers that are divisible by 11.

3. Calculating the Probability: - The probability can be calculated as the ratio of the count of numbers divisible by 11 to the total possible three-digit numbers.

Counting the Numbers Divisible by 11

To find the count of three-digit numbers that are divisible by 11, we can use the divisibility rule for 11, which states that the difference between the sum of the digits at odd places and the sum of the digits at even places should be either 0 or a multiple of 11.

Using this rule, we can count the numbers that satisfy this condition.

Calculating the Probability

After finding the count of numbers divisible by 11, we can calculate the probability using the formula:

\[ \text{Probability} = \frac{\text{Count of Numbers Divisible by 11}}{\text{Total Possible Three-Digit Numbers}} \]

Let's proceed with the calculation.