Question

Чтобы пройти в следующий круг соревнований, футбольной команде нужно набрать хотя бы 8 очков в двух играх. Если команда выигрывает, то получает 5 очков, ничья - 3 очка, проигрыш - 0 очков. Найти вероятность того, что команде удастся выйти в следующий круг соревнований. Считайте, что в каждой игре вероятности выигрыша и проигрыша одинаковы и равны 0,2.

Answer 1

1 выигрыш и 1 ничья и вот тебе ответ

Answer 2

Calculation of the Probability

To calculate the probability of the football team advancing to the next round of the competition, we need to consider the different outcomes in the two games.

According to the given information, if the team wins a game, they receive 5 points, a draw earns them 3 points, and a loss gives them 0 points. The team needs to accumulate at least 8 points in the two games to advance.

Let's calculate the probability step by step:

1. Win-Win Scenario: The team wins both games. The probability of winning a game is given as 0.2. Therefore, the probability of winning both games is 0.2 * 0.2 = 0.04.

2. Win-Draw Scenario: The team wins one game and draws the other. The probability of winning a game is 0.2, and the probability of a draw is 0.3. Therefore, the probability of winning one game and drawing the other is 0.2 * 0.3 + 0.3 * 0.2 = 0.12.

3. Draw-Win Scenario: The team draws one game and wins the other. This scenario is the same as the previous one, so the probability is also 0.12.

4. Draw-Draw Scenario: The team draws both games. The probability of a draw is 0.3. Therefore, the probability of drawing both games is 0.3 * 0.3 = 0.09.

5. Lose-Win Scenario: The team loses one game and wins the other. The probability of losing a game is 0.8 (1 - 0.2). Therefore, the probability of losing one game and winning the other is 0.8 * 0.2 = 0.16.

6. Win-Lose Scenario: The team wins one game and loses the other. This scenario is the same as the previous one, so the probability is also 0.16.

7. Lose-Lose Scenario: The team loses both games. The probability of losing a game is 0.8. Therefore, the probability of losing both games is 0.8 * 0.8 = 0.64.

To find the overall probability, we add up the probabilities of all the favorable scenarios:

0.04 + 0.12 + 0.12 + 0.09 + 0.16 + 0.16 + 0.64 = 1.33

However, the total probability should not exceed 1. Therefore, the probability of the team advancing to the next round is 1.

Please note that the given probabilities are assumed to be independent and equal for each game.