Question

Перед началом первого тура чемпионата по теннису участников разбивают на игровые пары случайным образом с помощью жребия.всего в чемпионате участвует 76 теннисистов, среди которых 7 спортсменов из России, в том числе Анатолий Москвин.Найдите вероятность того, что в первом туре Анатолий Москвин будет играть с каким-либо теннисистом из России.

Answer 1

соперников из РФ 7-1=6

всего соперников 76-1=75

Р(А)=6/75=0,08

Ответ: 0,08

Answer 2

76-1=75

7-1=6

6/75=0,08

Answer 3

Probability of Anatoly Moskvin playing against a Russian tennis player in the first round

To find the probability of Anatoly Moskvin playing against a Russian tennis player in the first round, we need to consider the total number of possible pairings and the number of pairings that include Anatoly Moskvin and a Russian player.

Given that there are 76 participants in the tournament, including 7 Russian players, we can calculate the total number of possible pairings using the combination formula:

Total number of possible pairings = C(76, 2) = 76! / (2! * (76-2)!)

Next, we need to calculate the number of pairings that include Anatoly Moskvin and a Russian player. Since Anatoly Moskvin is one of the 76 participants and there are 7 Russian players, the number of pairings that include Anatoly Moskvin and a Russian player is:

Number of pairings with Anatoly Moskvin and a Russian player = C(1, 1) * C(7, 1) = 1 * 7 = 7

Finally, we can calculate the probability by dividing the number of pairings with Anatoly Moskvin and a Russian player by the total number of possible pairings:

Probability = Number of pairings with Anatoly Moskvin and a Russian player / Total number of possible pairings

Plugging in the values, we get:

Probability = 7 / (76! / (2! * (76-2)!))

Now, let's calculate the probability using the given values.

Probability = 7 / (76! / (2! * (76-2)!))

Probability = 7 / (76! / (2! * 74!))

Probability = 7 / (76 * 75 / 2)

Probability = 7 / (5700 / 2)

Probability = 7 / 2850

Probability ≈ 0.00245614035

Therefore, the probability of Anatoly Moskvin playing against a Russian tennis player in the first round is approximately 0.00245614035.

Please note that the above calculation assumes that the pairings are truly random and that there are no other factors influencing the pairings.