Question

Из колоды в 36 карт одновременно вытаскивают 2 карты. Найдите вероятность того, что:а) обе они черной мастиб) обе они пикив) обе они трефыг) одна из них пиковой масти, а другая трефовой мастиРешение должно быть с пояснениями

Answer 1

А) В колоде 18 карт чёрной масти. Вероятность вытащить в первый раз черную масть равна 18/36 = 1/2. После этого в колоде останется 35 карт, из них 17 чёрной масти. Поэтому вероятность вытащить во второй раз карту чёрной масти равна 17/35. Т.к. события вытаскивания карт не связаны между собой, то общая вероятность вытащить две карты подряд чёрной масти равна произведению вероятностей, т.е. 1/2 * 17/35 = 17/70.

б) В колоде 9 карт пик. Аналогично, как в пункте а) считаем вероятность вытащить две пиковые карты. В первый раз - 9/36 = 1/4. Во второй раз - 8/35. Общая вероятность равна 1/4 * 8/35 = 2/35.

в) В колоде 9 карт треф. Решение и результат аналогичен пункту б), т.е. 2/35.

г) В колоде пиковых и трефовых карт по 9 штук. Вытаскиваем в первый раз, допустим, пиковую карту. Вероятность этого события равна 9/36 = 1/4. Вероятность вытащить вторую карту трефовой масти равна 9/35. Т.к. число карт уменьшилось на 1, а трефовых карт как было 9, так и осталось 9 карт. Общая вероятность равна 1/4 * 9/35 = 9/140.
Если поменять местами порядок вытаскивания этих двух карт, то ничего не изменится.

Answer 2

Probability of drawing two black cards

To find the probability of drawing two black cards from a deck of 36 cards, we need to determine the number of favorable outcomes (drawing two black cards) and the total number of possible outcomes.

In a deck of 36 cards, there are 18 black cards (9 spades and 9 clubs) and 18 red cards (9 hearts and 9 diamonds).

The total number of possible outcomes is the number of ways to choose 2 cards from a deck of 36 cards, which can be calculated using the combination formula:

Total number of possible outcomes = C(36, 2) = 36! / (2! * (36-2)!) = 630

The number of favorable outcomes is the number of ways to choose 2 black cards from the 18 black cards in the deck:

Number of favorable outcomes = C(18, 2) = 18! / (2! * (18-2)!) = 153

Therefore, the probability of drawing two black cards is:

Probability = Number of favorable outcomes / Total number of possible outcomes = 153 / 630 ≈ 0.243

So, the probability of drawing two black cards from a deck of 36 cards is approximately 0.243.

Probability of drawing two spades

To find the probability of drawing two spades from a deck of 36 cards, we need to determine the number of favorable outcomes (drawing two spades) and the total number of possible outcomes.

In a deck of 36 cards, there are 9 spades.

The total number of possible outcomes is the number of ways to choose 2 cards from a deck of 36 cards, which we calculated earlier as 630.

The number of favorable outcomes is the number of ways to choose 2 spades from the 9 spades in the deck:

Number of favorable outcomes = C(9, 2) = 9! / (2! * (9-2)!) = 36

Therefore, the probability of drawing two spades is:

Probability = Number of favorable outcomes / Total number of possible outcomes = 36 / 630 ≈ 0.057

So, the probability of drawing two spades from a deck of 36 cards is approximately 0.057.

Probability of drawing two clubs

To find the probability of drawing two clubs from a deck of 36 cards, we need to determine the number of favorable outcomes (drawing two clubs) and the total number of possible outcomes.

In a deck of 36 cards, there are 9 clubs.

The total number of possible outcomes is the number of ways to choose 2 cards from a deck of 36 cards, which we calculated earlier as 630.

The number of favorable outcomes is the number of ways to choose 2 clubs from the 9 clubs in the deck:

Number of favorable outcomes = C(9, 2) = 9! / (2! * (9-2)!) = 36

Therefore, the probability of drawing two clubs is:

Probability = Number of favorable outcomes / Total number of possible outcomes = 36 / 630 ≈ 0.057

So, the probability of drawing two clubs from a deck of 36 cards is approximately 0.057.

Probability of drawing one spade and one club

To find the probability of drawing one spade and one club from a deck of 36 cards, we need to determine the number of favorable outcomes (drawing one spade and one club) and the total number of possible outcomes.

In a deck of 36 cards, there are 9 spades and 9 clubs.

The total number of possible outcomes is the number of ways to choose 2 cards from a deck of 36 cards, which we calculated earlier as 630.

The number of favorable outcomes is the number of ways to choose 1 spade from the 9 spades and 1 club from the 9 clubs in the deck:

Number of favorable outcomes = C(9, 1) * C(9, 1) = 9 * 9 = 81

Therefore, the probability of drawing one spade and one club is:

Probability = Number of favorable outcomes / Total number of possible outcomes = 81 / 630 ≈ 0.129

So, the probability of drawing one spade and one club from a deck of 36 cards is approximately 0.129.

Probability of drawing one spade and one club

To find the probability of drawing one spade and one club from a deck of 36 cards, we need to determine the number of favorable outcomes (drawing one spade and one club) and the total number of possible outcomes.

In a deck of 36 cards, there are 9 spades and 9 clubs.

The total number of possible outcomes is the number of ways to choose 2 cards from a deck of 36 cards, which we calculated earlier as 630.

The number of favorable outcomes is the number of ways to choose 1 spade from the 9 spades and 1 club from the 9 clubs in the deck:

Number of favorable outcomes = C(9, 1) * C(9, 1) = 9 * 9 = 81

Therefore, the probability of drawing one spade and one club is:

Probability = Number of favorable outcomes / Total number of possible outcomes = 81 / 630 ≈ 0.129

So, the probability of drawing one spade and one club from a deck of 36 cards is approximately 0.129.