Question

В группе из 25 студентов имеется 11 отличников. Выбираются наудачу три студента. Какова вероятность, что все они отличники

Answer 1

Неуверен что пишу правильное решения,но я думаю так
11-отличники
14-не отличники
25-всего
выбирается 3 шт следовательно 25+11=36  и затем 3/36=1/12

Answer 2

Probability of selecting three excellent students from a group of 25 students

To calculate the probability of selecting three excellent students from a group of 25 students, we need to determine the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes is the total number of ways to choose three students from a group of 25. This can be calculated using the combination formula:

Total number of possible outcomes = C(25, 3)

The number of favorable outcomes is the number of ways to choose three excellent students from a group of 11 excellent students. This can be calculated using the combination formula as well:

Number of favorable outcomes = C(11, 3)

The probability of selecting three excellent students can then be calculated by dividing the number of favorable outcomes by 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: Using the combination formula, we have: C(25, 3) = 25! / (3! * (25 - 3)!) = 25! / (3! * 22!) = (25 * 24 * 23) / (3 * 2 * 1) = 2300

Number of favorable outcomes: Using the combination formula, we have: C(11, 3) = 11! / (3! * (11 - 3)!) = 11! / (3! * 8!) = (11 * 10 * 9) / (3 * 2 * 1) = 165

Probability: Probability = Number of favorable outcomes / Total number of possible outcomes = 165 / 2300 ≈ 0.0717

Therefore, the probability of selecting three excellent students from a group of 25 students is approximately 0.0717 or 7.17%.