Question

Из колоды карт (36 листов) случайным образом выбираются 4. Какова вероятность, что все среди выбранных карт ровно 2 туза?

Answer 1

ЧИСЛО КАРТ ПАДИЛИТЬ НА ПРАЦЕНТ 36 ВНИЗУ 4 В ВЕРХУ

Answer 2

Problem Analysis

We have a deck of 36 cards, and we randomly select 4 cards from the deck. We want to find the probability that exactly 2 of the selected cards are aces.

Solution

To solve this problem, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

Total Number of Possible Outcomes: The total number of possible outcomes is the number of ways we can select 4 cards from a deck of 36 cards. This can be calculated using the combination formula:

C(n, k) = n! / (k! * (n - k)!)

Where: - n is the total number of cards in the deck (36 in this case) - k is the number of cards we want to select (4 in this case)

Using this formula, we can calculate the total number of possible outcomes.

Number of Favorable Outcomes: The number of favorable outcomes is the number of ways we can select 2 aces from the 4 selected cards. Since there are 4 aces in the deck, we can calculate this using the combination formula as well:

C(4, 2) = 4! / (2! * (4 - 2)!)

Using this formula, we can calculate the number of favorable outcomes.

Probability Calculation: Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

Let's calculate the probability.

Calculation

The total number of possible outcomes can be calculated as follows:

C(36, 4) = 36! / (4! * (36 - 4)!) = 36! / (4! * 32!) = (36 * 35 * 34 * 33) / (4 * 3 * 2 * 1) = 58905

The number of favorable outcomes can be calculated as follows:

C(4, 2) = 4! / (2! * (4 - 2)!) = 4! / (2! * 2!) = (4 * 3) / (2 * 1) = 6

Therefore, the probability of selecting exactly 2 aces from the 4 selected cards is:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes = 6 / 58905 ≈ 0.000102

So, the probability is approximately 0.000102, or about 0.0102%.

Answer

The probability of selecting exactly 2 aces from a randomly selected set of 4 cards from a deck of 36 cards is approximately 0.000102, or about 0.0102%.