Question

Если шахматист А. играет белыми фигурами, то он выигрывает у шахматиста Б. с вероятностью 0,5. Если А. играет чёрными, то А. выигрывает у Б. с вероятностью 0,32. Шахматисты А. и Б. играют две партии, причём во второй партии меняют цвет фигур. Найдите вероятность того, что А. выиграет ровно один раз.

Answer 1

Событие - выиграл ОДИН раз - это два варианта.
Выиграл в первой игре -  р1 = 0,5
Вероятность проиграть в первой игре -  q1 = 1 - p1 = 0.5.
ИЛИ - в первой проиграл, но выиграл во второй - Р =q1*p2 = 0.5*0.32 = 0.16.

Вероятности событий - ИЛИ - суммируются - 0,5+ 0,32 = 0,82 = 82%-ОТВЕТ

Answer 2

Calculation of the Probability

To find the probability that player A wins exactly one game out of the two games they play, we need to consider two scenarios:

1. Player A wins the first game and loses the second game. 2. Player A loses the first game and wins the second game.

Let's calculate the probability for each scenario separately and then add them together.

Scenario 1: Player A wins the first game and loses the second game

The probability that player A wins the first game while playing as white is 0.5 The probability that player A loses the second game while playing as black is 0.68 (1 - 0.32).

To calculate the probability of both events happening, we multiply the probabilities together:

Probability of Scenario 1 = Probability of A winning as white * Probability of A losing as black = 0.5 * 0.68 = 0.34

Scenario 2: Player A loses the first game and wins the second game

The probability that player A loses the first game while playing as white is 0.5 The probability that player A wins the second game while playing as black is 0.32.

To calculate the probability of both events happening, we multiply the probabilities together:

Probability of Scenario 2 = Probability of A losing as white * Probability of A winning as black = 0.5 * 0.32 = 0.16

Total Probability

To find the total probability that player A wins exactly one game, we add the probabilities of the two scenarios together:

Total Probability = Probability of Scenario 1 + Probability of Scenario 2 = 0.34 + 0.16 = 0.5

Therefore, the probability that player A wins exactly one game out of the two games they play is 0.5.

Please note that the probabilities used in this calculation are taken from the search result snippets