Question

Колода игральных карт из 52 листов тщательно перетасована. Наудачу берут 4 карты. Найти вероятность того, что среди этих карт окажутся представители всех четырех мастей

Answer 1

Ответ:

Пошаговое объяснение:

1) Первая карта нам нужна любая, потому что не скащано, с какой масти мы должны начать, значит 52/52=1 верояность вытащить любую 2) каждой масти по 13 карт в колоде. Одна масть у нас уже есть, значит, нам надо вытащить 39 карт (13*3масти) из оставшихся 51 карты. 39/51=13/17= 0,76 вероятность вытащить вторую карту второй масти. 3) осталось 2 вида масти и 50 карт в колоде. 26/50=13/25=0,52 4) 13/49=0,27 5)1*0,76*0,52*0,27=0,11. Ответ: 0,11 вероятность вытащить 4 карты разной масти

Answer 2

Probability of drawing representatives from all four suits

To find the probability of drawing representatives from all four suits when randomly selecting 4 cards from a well-shuffled deck of 52 cards, we can use the concept of combinations.

The total number of ways to choose 4 cards from a deck of 52 cards is given by the combination formula:

C(n, r) = n! / (r!(n-r)!)

Where: - n is the total number of items (52 cards in a deck) - r is the number of items to be chosen (4 cards in this case) - ! denotes the factorial operation

In this case, we want to find the number of ways to choose 4 cards such that representatives from all four suits are included. There are 4 suits in a deck of cards: hearts, diamonds, clubs, and spades.

Let's calculate the probability step by step:

1. Calculate the number of ways to choose 1 card from each suit: - For each suit, there are 13 cards (Ace, 2-10, Jack, Queen, King). - So, the number of ways to choose 1 card from each suit is 13 * 13 * 13 * 13 = 285,616.

2. Calculate the total number of ways to choose 4 cards from the deck: - Using the combination formula, C(52, 4) = 52! / (4!(52-4)!) = 270,725.

3. Calculate the probability: - The probability is given by the number of favorable outcomes (choosing representatives from all four suits) divided by the total number of possible outcomes. - So, the probability is 285,616 / 270,725 ≈ 0.1054, or approximately 10.54%.

Therefore, the probability of randomly selecting 4 cards from a well-shuffled deck and having representatives from all four suits is approximately 10.54%.