Question

Чтобы пройти в следующий круг соревнований, шахматисту нужно набрать хотя бы 1,5 очка по итогам двух игр. Если шахматист выигрывает, он получает 1 очко, в случае ничьей - 0,5 очка, если проигрывает - 0 очков. Найдите вероятность того, что шахматисту удастся выйти в следующий круг соревнований. Считайте, что в каждой игре вероятность выигрыша и проигрыша одинакова и равна 0,3.

Answer 1

Вероятность ничьей-0.4
0.4*0.3=0.12

Answer 2

Calculation of the Probability

To calculate the probability of a chess player advancing to the next round of the competition, we need to consider the possible outcomes of the two games and their corresponding probabilities.

Let's denote the probability of winning a game as P(win), the probability of a draw as P(draw), and the probability of losing as P(loss). According to the given information, P(win) = 0.3, P(draw) = 0.3, and P(loss) = 0.4.

To advance to the next round, the chess player needs to score at least 1.5 points. Let's consider the possible ways to achieve this:

1. Winning both games: The player receives 1 point for each win, so the total score would be 2 points. 2. Winning one game and drawing the other: The player receives 1 point for the win and 0.5 points for the draw, resulting in a total score of 1.5 points.

To calculate the probability of each outcome, we can multiply the probabilities of the individual events.

The probability of winning both games is P(win) * P(win) = 0.3 * 0.3 = 0.09.

The probability of winning one game and drawing the other can be calculated in two ways: - Winning the first game and drawing the second: P(win) * P(draw) = 0.3 * 0.3 = 0.09. - Drawing the first game and winning the second: P(draw) * P(win) = 0.3 * 0.3 = 0.09.

Adding these two probabilities together, we get 0.09 + 0.09 = 0.18.

Therefore, the probability that the chess player will advance to the next round of the competition is 0.09 + 0.18 = 0.27 or 27%.