Question

В очереди в библиотеку стоят 30 студентов. Среди них Иванов и Петров. Найти вероятность, что между ними стоят ровно 1 других студентов.

Answer 1

Вероятность того что Петров или Иванов стоят через одного в этой цепи, получаем m=2; n=29
P(A) = m/n=2/29
Если разорвать цепь не между Ивановым и Петровым, то вероятность m=28; n=30; P(B)=28/30
По правилу произведения
 2/29 * 28/30 = 28/(29*15) = 28/435 ≈ 0.064

Answer 2

Problem Statement

In a library queue, there are 30 students waiting in line. Among them are Ivanov and Petrov. We need to find the probability that there is exactly 1 other student standing between them.

Solution

To find the probability, we need to calculate the number of favorable outcomes (the number of ways Ivanov and Petrov can have exactly 1 student between them) and the total number of possible outcomes (the total number of ways the 30 students can be arranged in the queue).

Let's break down the problem into steps:

1. Calculate the total number of possible outcomes: - Since there are 30 students in total, the total number of possible outcomes is the number of ways to arrange these 30 students in a line, which is given by the factorial of 30 (30!). - Total number of possible outcomes = 30!

2. Calculate the number of favorable outcomes: - To have exactly 1 student between Ivanov and Petrov, we can consider them as a single entity. - So, we have 29 entities (28 students + Ivanov and Petrov) that need to be arranged in the queue. - The number of ways to arrange these 29 entities is given by the factorial of 29 (29!). - However, Ivanov and Petrov can switch places, so we need to multiply the result by 2. - Number of favorable outcomes = 2 * 29!

3. Calculate the probability: - The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. - Probability = Number of favorable outcomes / Total number of possible outcomes

Let's calculate the probability:

Total number of possible outcomes = 30! = 265252859812191058636308480000000

Number of favorable outcomes = 2 * 29! = 2 * 884176199373970195454361600000

Probability = (2 * 884176199373970195454361600000) / 265252859812191058636308480000000

Simplifying the expression, we get:

Probability = 1 / 150515293936127026918161280000

Therefore, the probability that there is exactly 1 other student standing between Ivanov and Petrov is approximately 6.64 x 10^-30.

Please note that the above calculation assumes that all the students are distinct and can be arranged in any order. If there are any additional constraints or assumptions, please let me know.

Conclusion

The probability that there is exactly 1 other student standing between Ivanov and Petrov in the library queue of 30 students is approximately 6.64 x 10^-30.