Question

Для участия в шахматном турнире записалось 20 человек. Организаторы отобрали из них команду в 9 человек. Какова вероятность того, что два наиболее сильных шахматиста попадут в команду б)только один наиболее сильный шахматист попадет в команду.

Answer 1

1)50на50,2)50на50. наверное

Answer 2

Calculation of Probability

To calculate the probability of the two strongest chess players being selected for the team, we need to consider the total number of possible teams that can be formed from the pool of 20 participants.

The total number of ways to select a team of 9 people from a pool of 20 participants can be calculated using the combination formula:

C(n, r) = n! / (r!(n-r)!)

Where: - n is the total number of participants (20 in this case) - r is the number of people to be selected for the team (9 in this case) - ! denotes the factorial operation

Let's calculate the probability for both scenarios:

Scenario 1: Both strongest chess players are selected

To calculate the probability of both strongest chess players being selected for the team, we need to consider that there are 2 strongest players out of the 20 participants.

The probability can be calculated as the number of ways to select the 2 strongest players out of 20 divided by the total number of ways to select a team of 9 people from 20 participants.

Probability = (Number of ways to select 2 strongest players) / (Total number of ways to select a team of 9)

Number of ways to select 2 strongest players = C(2, 2) = 1 (since there are only 2 strongest players)

Total number of ways to select a team of 9 = C(20, 9) = 167,960

Probability = 1 / 167,960

Scenario 2: Only one strongest chess player is selected

To calculate the probability of only one strongest chess player being selected for the team, we need to consider that there are 2 strongest players out of the 20 participants.

The probability can be calculated as the number of ways to select 1 strongest player out of 2 multiplied by the number of ways to select the remaining 8 players out of the remaining 18 participants, divided by the total number of ways to select a team of 9 people from 20 participants.

Probability = (Number of ways to select 1 strongest player) * (Number of ways to select 8 remaining players) / (Total number of ways to select a team of 9)

Number of ways to select 1 strongest player = C(2, 1) = 2

Number of ways to select 8 remaining players = C(18, 8) = 437,586

Probability = (2 * 437,586) / 167,960

Now, let's calculate the probabilities:

Calculation:

Probability of both strongest players being selected: Probability = 1 / 167,960

Probability of only one strongest player being selected: Probability = (2 * 437,586) / 167,960

Please note that the probabilities are calculated based on the assumption that the selection process is random and all participants have an equal chance of being selected.