Question

Из колоды в 36 карт наудачу отбирают 5. Найти вероятность того, что все они красные.

Answer 1

1/2*17/35*16/34*15/33*14/32

Answer 2

Problem Statement

We are given a deck of 36 cards, and we randomly select 5 cards from the deck. We need to find the probability that all 5 selected cards are red.

Solution

To find the probability, we need to determine the total number of favorable outcomes (i.e., the number of ways to select 5 red cards) and the total number of possible outcomes (i.e., the total number of ways to select any 5 cards from the deck).

# Total Number of Favorable Outcomes

The deck consists of 36 cards, and we want to select 5 red cards. We can calculate the number of ways to select 5 red cards from the 18 red cards in the deck using the combination formula:

Number of ways to select 5 red cards = C(18, 5)

# Total Number of Possible Outcomes

We want to select any 5 cards from the deck of 36 cards. We can calculate the number of ways to select any 5 cards from the deck using the combination formula:

Number of ways to select any 5 cards = C(36, 5)

# Probability Calculation

The probability of selecting all 5 red cards can be calculated by dividing the number of favorable outcomes by the number of possible outcomes:

Probability = (Number of ways to select 5 red cards) / (Number of ways to select any 5 cards)

Let's calculate the probability using the combination formula:

Number of ways to select 5 red cards = C(18, 5) = 8568

Number of ways to select any 5 cards = C(36, 5) = 376,992

Probability = 8568 / 376,992 ≈ 0.0227

Therefore, the probability that all 5 selected cards are red is approximately 0.0227.