Question

Из колоды в 36 карт вытаскивают 4 карты. Какова вероятность, что будут вынуты 2 короля и 2 дамы?

Answer 1

Ответ:

Пошаговое объяснение:

0.2％вероятность того что окажется 2короля и 2дамы

Answer 2

Calculating the Probability

To calculate the probability of drawing 2 kings and 2 queens from a deck of 36 cards, we need to determine the total number of favorable outcomes and the total number of possible outcomes.

The total number of possible outcomes is the number of ways to choose 4 cards from a deck of 36. This can be calculated using the combination formula:

Total number of possible outcomes = C(36, 4)

The total number of favorable outcomes is the number of ways to choose 2 kings from the 4 available kings and 2 queens from the 4 available queens. This can be calculated using the combination formula as well:

Total number of favorable outcomes = C(4, 2) * C(4, 2)

Finally, the probability can be calculated by dividing the total number of favorable outcomes by the total number of possible outcomes:

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

Let's calculate the probability step by step.

Step 1: Calculate the total number of possible outcomes

Using the combination formula, we can calculate the total number of possible outcomes as follows:

Total number of possible outcomes = C(36, 4) = 36! / (4! * (36-4)!)

Calculating this value gives us:

Total number of possible outcomes = 36! / (4! * 32!) = 36 * 35 * 34 * 33 / (4 * 3 * 2 * 1) = 58905

Step 2: Calculate the total number of favorable outcomes

Using the combination formula, we can calculate the total number of favorable outcomes as follows:

Total number of favorable outcomes = C(4, 2) * C(4, 2) = (4! / (2! * (4-2)!)) * (4! / (2! * (4-2)!))

Calculating this value gives us:

Total number of favorable outcomes = (4! / (2! * 2!)) * (4! / (2! * 2!)) = (4 * 3 / (2 * 1)) * (4 * 3 / (2 * 1)) = 36

Step 3: Calculate the probability

Now that we have the total number of favorable outcomes and the total number of possible outcomes, we can calculate the probability:

Probability = Total number of favorable outcomes / Total number of possible outcomes = 36 / 58905

Calculating this value gives us:

Probability ≈ 0.0006119

Therefore, the probability of drawing 2 kings and 2 queens from a deck of 36 cards is approximately 0.0006119, or about 0.06119%.