Question

В классе 6 учащихся,среди них два друга-Михаил и Вадим.Класс случайным образом разбивают на 3 равные группы.Найти вероятность,что М и В окажутся в одной группе.

Answer 1

В 1-й группе 2. человека, а т к одно место занял Вадим, то остается 1- это благоприятный исход для Михаила
а всего исходов 5, одно занято
1/5=0,2

Answer 2

Problem Analysis

We are given a class of 6 students, including two friends named Mikhail and Vadim. The class is randomly divided into 3 equal groups. We need to find the probability that Mikhail and Vadim end up in the same group.

Solution

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

# Total Number of Outcomes

Since the class is randomly divided into 3 equal groups, we can calculate the total number of outcomes using the concept of combinations. We need to choose 2 groups out of 3 for Mikhail and Vadim, and the remaining group will automatically have the other 4 students. The total number of outcomes can be calculated as:

Total number of outcomes = Number of ways to choose 2 groups out of 3 = C(3, 2) = 3

# Number of Favorable Outcomes

To calculate the number of favorable outcomes, we need to determine the number of ways Mikhail and Vadim can be placed in the same group. Since there are 3 groups, there are 3 possible ways for Mikhail and Vadim to be in the same group:

1. Mikhail and Vadim are in Group 1, and the remaining 4 students are divided into Groups 2 and 3. 2. Mikhail and Vadim are in Group 2, and the remaining 4 students are divided into Groups 1 and 3. 3. Mikhail and Vadim are in Group 3, and the remaining 4 students are divided into Groups 1 and 2.

Therefore, the number of favorable outcomes is 3.

# Probability Calculation

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:

Probability = Number of favorable outcomes / Total number of outcomes = 3 / 3 = 1

So, the probability that Mikhail and Vadim end up in the same group is 1 or 100%.

Conclusion

The probability that Mikhail and Vadim end up in the same group when the class is randomly divided into 3 equal groups is 100%. This means that it is certain that they will be in the same group.

Note: The sources provided did not contain relevant information for this specific problem.