Question

Если гроссмейстер А. играет белыми, то он выигрывает у гроссмейстера Б. с вероятностью 0,5. Если А. играет черными, то А. выигрывает у Б. с вероятностью 0,3. Гроссмейстеры А. и Б. играют две партии, причем во второй партии меняют цвет фигур. Найдите вероятность того, что А. выиграет хотя бы одну партию.

Answer 1

Сначала находим вероятность того,что гроссмейстер не выиграет ни одну партию: 0,5*0,7=0,35.Далее p=1-0,35=0,65

Answer 2

Problem Analysis

We are given that if Grandmaster A plays as white, they win against Grandmaster B with a probability of 0.5. If A plays as black, they win against B with a probability of 0.3. A and B play two games, and in the second game, the colors are switched. We need to find the probability that A wins at least one game.

Solution

To find the probability that A wins at least one game, we can find the probability that A loses both games and subtract it from 1.

Let's calculate the probability that A loses both games: - The probability that A loses the first game as white is 1 - 0.5 = 0.5. - The probability that A loses the second game as black is 1 - 0.3 = 0.7.

The probability that A loses both games is the product of these probabilities: 0.5 * 0.7 = 0.35.

Therefore, the probability that A wins at least one game is 1 - 0.35 = 0.65.

Answer

The probability that Grandmaster A wins at least one game against Grandmaster B is 0.65.