Question

В соревновании участвуют 8 человек. Какова вероятность того, что будет верно предсказана тройка призеров?

Answer 1

Ответ:

Пошаговое объяснение:

Призёров всего 3 ,всего людей 8 .

3 : 8 = 0,375

Ответ : 0,375

Answer 2

Calculation of the Probability of Predicting the Top Three Winners

To calculate the probability of correctly predicting the top three winners in a competition with 8 participants, we need to consider the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes is the number of ways we can arrange the 8 participants in the competition. This can be calculated using the concept of permutations, which is denoted by nPk and calculated as n! / (n-k)!. In this case, we have 8 participants and we want to arrange them in groups of 3, so the total number of possible outcomes is 8P3.

The number of favorable outcomes is the number of ways we can select the top three winners from the 8 participants. This can be calculated using the concept of combinations, which is denoted by nCk and calculated as n! / (k!(n-k)!). In this case, we have 8 participants and we want to select 3 winners, so the number of favorable outcomes is 8C3.

Now, let's calculate the probability of correctly predicting the top three winners.

Calculation:

The total number of possible outcomes (arrangements) is given by 8P3: 8P3 = 8! / (8-3)! = 8! / 5! = 8 * 7 * 6 = 336

The number of favorable outcomes (selections) is given by 8C3: 8C3 = 8! / (3!(8-3)!) = 8! / (3! * 5!) = 8 * 7 * 6 / (3 * 2 * 1) = 56

Therefore, the probability of correctly predicting the top three winners is the number of favorable outcomes divided by the total number of possible outcomes: Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes = 56 / 336 = 1 / 6 ≈ 0.1667

So, the probability of correctly predicting the top three winners in the competition is approximately 0.1667 or 16.67%.

Please note that the above calculation assumes that all participants have an equal chance of winning and that the order of the winners matters.