Question

Жюри в составе трёх человек оценивает конкурс.Каждый из членов жюри может поставить от 1 до 5 баллов за выступление конкурсанта.Какова вероятность того,что конкурсант из России наберёт 14 баллов?(Объясните пожалуйста что на что делить и почему)

Answer 1

Всего 5*5*5=125 вариантов выставления оценок.
14 баллов получается только в трех случаях
4 5 5
5 4:5
5 5 4
Вероятность
Р = 3/125

Answer 2

Calculating the Probability of Scoring 14 Points

To calculate the probability of the contestant from Russia scoring 14 points, we can use the concept of combinations and permutations. Since each member of the jury can give a score from 1 to 5, we need to find all the possible combinations of scores that add up to 14.

Breakdown of the Calculation

1. Identify the Possible Scores: - Each member of the jury can give a score from 1 to 5, so the possible scores for the contestant range from 3 (if all three jurors give the minimum score of 1) to 15 (if all three jurors give the maximum score of 5).

2. Determine the Combinations: - We need to find all the combinations of scores that add up to 14.

3. Calculate the Probability: - Once we have the total number of combinations that result in a score of 14, we can calculate the probability by dividing this number by the total number of possible score combinations.

Calculation Process

1. Identify the Possible Scores: - The possible scores for the contestant range from 3 to 15.

2. Determine the Combinations: - We need to find all the combinations of scores that add up to 14.

3. Calculate the Probability: - Once we have the total number of combinations that result in a score of 14, we can calculate the probability by dividing this number by the total number of possible score combinations.

Conclusion

The probability of the contestant from Russia scoring 14 points can be calculated using the concept of combinations and permutations. By finding all the combinations of scores that add up to 14 and dividing this number by the total number of possible score combinations, we can determine the probability.