Question

В группе 20 студентов,среди которых 10 отличников.По списку наудачу отобраны 12 студентов.Найдите вероятность того, что среди них пять отличников.

Answer 1

Вероятность с с элементами комбинаторики.

Answer 2

Calculating the Probability of Selecting Five Honor Students

To calculate the probability of randomly selecting five honor students out of the 12 students chosen from a group of 20, we can use the concept of combinations.

Total Number of Students: 20 Number of Honor Students: 10 Number of Students Selected: 12 Number of Honor Students to be Selected: 5

Using Combinations to Calculate the Probability

The formula for calculating combinations is:

nCr = n! / (r! * (n-r)!)

Where: - n = total number of items - r = number of items to be chosen - ! = factorial

Using this formula, we can calculate the number of ways to choose 5 honor students out of 10, and the number of ways to choose 7 non-honor students out of 10.

Calculating the Probability

The probability can then be calculated using the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

We can use the results of the combinations to determine the probability of selecting five honor students out of the 12 students chosen randomly from the group of 20.

Conclusion

By applying the concept of combinations and probability, we can determine the likelihood of selecting a specific number of honor students from the group of 12 students chosen randomly from the larger group of 20.