Question

ПОМОГИТЕ ПОЖАЛУЙСТА !!!! 35 БАЛЛОВ Всех 16 участников шахматного турнира можно разбить на три группы: группу сильнейших из 4 человек, группу средней силы из 8 человек и посредственную группу из 4 человек. Вероятность стать победителем для каждого шахматиста из сильнейшей группы одинакова и равна 0,15, из средней - 0,04, из посредственной - 0,02. Какова вероятность, что наудачу выбранный шахматист станет победителем турнира.

Answer 1

Probability of Winning the Tournament

To calculate the probability of a randomly chosen chess player winning the tournament, we need to consider the probabilities for each group and the number of players in each group.

According to the given information, there are three groups: - Group 1: The strongest group with 4 players. - Group 2: The intermediate group with 8 players. - Group 3: The average group with 4 players.

The probability of winning for each group is as follows: - Group 1: Probability = 0.15 - Group 2: Probability = 0.04 - Group 3: Probability = 0.02

To calculate the overall probability, we need to consider the number of players in each group. There are 16 players in total, with 4 players in Group 1, 8 players in Group 2, and 4 players in Group 3.

To find the probability of winning the tournament, we can use the weighted average of the probabilities for each group, where the weights are the number of players in each group.

Let's calculate the overall probability step by step:

1. Calculate the weighted probabilities for each group: - Group 1: Weighted Probability = Probability * Number of Players in Group = 0.15 * 4 = 0.6 - Group 2: Weighted Probability = Probability * Number of Players in Group = 0.04 * 8 = 0.32 - Group 3: Weighted Probability = Probability * Number of Players in Group = 0.02 * 4 = 0.08

2. Sum up the weighted probabilities for all groups: - Overall Probability = Sum of Weighted Probabilities = 0.6 + 0.32 + 0.08 = 1

Therefore, the probability of a randomly chosen chess player winning the tournament is 1 or 100%.

Please note that the given information does not provide any additional details or constraints that would affect the calculation of the overall probability.