Question

Колода из 36 карт разложена по мастям. из каждой масти выбирают по одной карте.какова вероятность что все четыре карты одинаковы"

Answer 1

Дано 36 карт, по 9 карт разного цвета красного, синего, зеленого, желтого, карты каждого цвета пронумерованы от 1 до 9. Наугад взяли из колоды 4 карты, все 4 оказались разного цвета. Какова вероятность события А = "Все 4 карты имеют одинаковый номер"?
Ответ: Р(А)=1/729.

Answer 2

Probability of all four cards being the same in a deck of 36 cards

To calculate the probability of all four cards being the same in a deck of 36 cards, we need to consider the number of favorable outcomes (the number of ways all four cards can be the same) and the total number of possible outcomes (the total number of ways four cards can be chosen from the deck).

In a deck of 36 cards, there are 4 suits (hearts, diamonds, clubs, and spades) and each suit has 9 cards (ace, 2, 3, 4, 5, 6, 7, 8, and 9). Since we are choosing one card from each suit, we need to calculate the probability of choosing the same card from each suit.

To calculate the probability, we can use the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

Let's calculate the probability step by step:

Step 1: Calculate the number of favorable outcomes: Since we need to choose one card from each suit, there is only one favorable outcome where all four cards are the same.

Number of favorable outcomes = 1

Step 2: Calculate the total number of possible outcomes: To calculate the total number of possible outcomes, we need to consider the number of ways we can choose one card from each suit.

Number of possible outcomes = Number of ways to choose a card from the first suit * Number of ways to choose a card from the second suit * Number of ways to choose a card from the third suit * Number of ways to choose a card from the fourth suit

Number of possible outcomes = 9 * 9 * 9 * 9 = 6561

Step 3: Calculate the probability: Now, we can calculate the probability using the formula mentioned earlier:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 6561

Therefore, the probability that all four cards are the same in a deck of 36 cards is approximately 0.0001526 or 0.01526%.

Please note that this calculation assumes that the deck is well-shuffled and each card has an equal chance of being selected.