Question

В классе 9 учащихся, среди них два друга - Олег и Андрей. Класс случайным образом разбивают на 3 равные группы. Найдите вероятность того, что Олег и Андрей окажутся в одной группе.

Answer 1

вероятность  этого равна 1к3

Answer 2

олег попал в одну группу - 3/9

андрей попал туда же 2/8

то что это одновременно 1/3*1/4=1/12

могло произойти в любой из 3 групп значит 1/12*3 =1/4

или 0.25

Answer 3

Calculating the Probability of Oleg and Andrey Being in the Same Group

To calculate the probability of Oleg and Andrey ending up in the same group after the class is randomly divided into 3 equal groups, we can use the following approach:

Total Number of Ways to Divide the Class: The total number of ways to divide the class into 3 equal groups can be calculated using the combination formula, which is given by: \[ C(n, r) = \frac{n!}{r!(n-r)!} \] Where: - n = total number of students in the class (9 in this case) - r = number of students in each group (3 in this case)

Number of Ways Oleg and Andrey Can Be in the Same Group: The number of ways Oleg and Andrey can be in the same group can be calculated by considering them as a single entity. This means we treat Oleg and Andrey as one unit and calculate the number of ways to divide the remaining 7 students and this unit into 3 groups.

Calculating the Probability: The probability of Oleg and Andrey being in the same group is then given by the ratio of the number of ways they can be in the same group to the total number of ways to divide the class into 3 equal groups.

Let's calculate the probability using the above approach.

Calculation

The total number of ways to divide the class of 9 students into 3 equal groups is given by: \[ C(9, 3) = \frac{9!}{3!(9-3)!} = 84 \]

The number of ways Oleg and Andrey can be in the same group is given by: \[ C(7, 3) = \frac{7!}{3!(7-3)!} = 35 \]

Therefore, the probability of Oleg and Andrey being in the same group is: \[ P = \frac{35}{84} \approx