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 оба раза. Ответ: ___________________________.

Answer 1

Calculation of the Probability of Player A Winning Both Games

To calculate the probability of Player A winning both games, we need to consider the probabilities of Player A winning when playing as white and when playing as black.

Let's denote the event of Player A winning as "W" and the event of Player A losing as "L."

Given the information provided, we know that: - If Player A plays as white, the probability of winning is 0.5. - If Player A plays as black, the probability of winning is 0.32.

To find the probability of Player A winning both games, we multiply the probabilities of winning each game together.

Let's calculate it step by step:

1. Probability of Player A winning as white: 0.5. 2. Probability of Player A winning as black: 0.32.

To find the probability of winning both games, we multiply these probabilities together:

0.5 * 0.32 = 0.16.

Therefore, the probability of Player A winning both games is 0.16.

Please note that this calculation assumes that the outcomes of the two games are independent events, meaning the result of one game does not affect the outcome of the other game.