Question

За круглый стол на 11 стульев в случайном порядке рассаживаются 9 мальчиков и 2 девочки. Найдите вероятность того, что обе девочки не будут сидеть рядом.

Answer 1

ВЕРОЯТНОСТЬ Р
Р=6/8=0.75 

ВЕРОЯТНОСТЬ ТОГО,ЧТО ОБЕ ДЕВОЧКИ НЕ БУДУТ СИДЕТЬ СИДЕТЬ РЯДОМ

Answer 2

Problem Analysis

We are given a round table with 11 chairs, and 9 boys and 2 girls are randomly seated. We need to find the probability that both girls will not be sitting next to each other.

Total Number of Arrangements

To find the total number of arrangements, we can consider the 11 chairs as distinct and the 11 people as distinguishable. The total number of arrangements is given by the formula for permutations, which is 11!.

Number of Arrangements with Girls Sitting Together

To find the number of arrangements where both girls are sitting together, we can treat the two girls as a single entity. This reduces the problem to arranging 10 entities (9 boys + 1 group of 2 girls) around the table. The number of arrangements with the girls sitting together is given by the formula for permutations, which is 10!.

Number of Arrangements with Girls Not Sitting Together

To find the number of arrangements where both girls are not sitting together, we can subtract the number of arrangements with the girls sitting together from the total number of arrangements.

Calculation

Let's calculate the probability using the formula:

Probability = Number of Arrangements with Girls Not Sitting Together / Total Number of Arrangements

The total number of arrangements is 11!, which is equal to 39,916,800.

The number of arrangements with the girls sitting together is 10!, which is equal to 3,628,800.

Therefore, the number of arrangements with the girls not sitting together is 11! - 10!, which is equal to 36,288,000.

Now we can calculate the probability:

Probability = 36,288,000 / 39,916,800 ≈ 0.909

So, the probability that both girls will not be sitting next to each other is approximately 0.909.

Answer

The probability that both girls will not be sitting next to each other is approximately 0.909.