Question

Два игрока подбрасывают монету. Один считает выпавшие орлы, другой решки. Выигрывает тот, кто первым наберет 20 очков. Сейчас счет 19:17 в пользу первого игрока. Какова вероятность, что он выиграет? (Ответ запишите в виде несократимой дроби a/b)

Answer 1

Найдем вероятность проигрыша первого игрока. Для этого необходимо, чтобы второй игрок сделал два выигрышных хода подряд (вероятность (1/2)^2 = 1/4), после чего с вероятностью 1/2 второй игрок выигрывает.

Таким образом вероятность проигрыша первого игрока составляет 1/4 * 1/2 = 1/8

А вероятность его выигрыша 1 - 1/8 = 7/8 

Answer 2

Мне кажется вероятность будет в виде неправильно дроби 19:17

Answer 3

Probability of Winning for the First Player

To determine the probability that the first player will win the game, we need to calculate the probability of the first player winning each individual coin toss and then sum up the probabilities until the first player reaches 20 points.

Given that the current score is 19:17 in favor of the first player, the first player needs only one more point to win, while the second player needs three more points.

Let's calculate the probability of the first player winning each coin toss:

- The probability of getting heads (or "орел") is 1/2. - The probability of getting tails (or "решка") is also 1/2.

Since the first player needs only one more point to win, they can achieve this by getting heads on the next coin toss. Therefore, the probability of the first player winning the game can be calculated as follows:

Probability of the first player winning = Probability of getting heads = 1/2.

Thus, the probability of the first player winning the game is 1/2.

Please note that the provided search results did not contain specific information about the probability calculation for this particular scenario. However, the probability of getting heads or tails in a fair coin toss is generally accepted as 1/2.

Therefore, the answer is 1/2.