Question

Перед началом первого тура чемпионате по теннису участников разбиваютна игровые пары случайный обраюм с помоющью жребия. Всего в чемпионате участвует 76 теннисистов, среди которых 7 спортсменов из России, в томчисле Анатолий Москвин. Найдите вероятность того, что в первом туреАнатолий Москвин будет играть с каким-либо тенниситом из россии

Answer 1

Всего участников - 76-1 = 75. Соперников из России : 7-1= 6. P(A) = n/m 6/75=0,08

Answer 2

Calculating the Probability of Anatoliy Moskvin Playing Against a Russian Player in the First Round of the Tennis Championship

To calculate the probability of Anatoliy Moskvin playing against a Russian player in the first round of the tennis championship, we can use the following approach:

1. Total Number of Possible Pairings: - The total number of possible pairings in the first round can be calculated using the combination formula: \[ C(n, r) = \frac{n!}{r!(n-r)!} \] - Where \( n = 76 \) (total number of tennis players) and \( r = 2 \) (number of players in each pairing).

2. Number of Pairings with Anatoliy Moskvin and a Russian Player: - We need to calculate the number of pairings where Anatoliy Moskvin plays against a Russian player.

3. Calculating the Probability: - The probability can then be calculated as the ratio of the number of favorable outcomes to the total number of possible pairings.

Let's proceed with the calculations.

Total Number of Possible Pairings:

The total number of possible pairings in the first round can be calculated using the combination formula: \[ C(76, 2) = \frac{76!}{2!(76-2)!} \] This will give us the total number of possible pairings in the first round.

Number of Pairings with Anatoliy Moskvin and a Russian Player:

The number of pairings where Anatoliy Moskvin plays against a Russian player can be calculated by considering the following: - There are 7 Russian players in the championship, including Anatoliy Moskvin. - Anatoliy Moskvin can be paired with any of the 6 other Russian players (excluding himself).

Calculating the Probability:

The probability of Anatoliy Moskvin playing against a Russian player in the first round can be calculated as: \[ \frac{\text{Number of pairings with Anatoliy Moskvin and a Russian player}}{\text{Total number of possible pairings}} \]

Let's calculate the probability.