Question

Из колоды в 36 карт наугад вынимают 5. Найти вероятность того, что среди них окажется хотя бы один туз

Answer 1

0,73, если это теория вероятности

Answer 2

Problem Statement

Из колоды в 36 карт наугад вынимают 5. Найти вероятность того, что среди них окажется хотя бы один туз.

Solution

To find the probability of drawing at least one ace from a deck of 36 cards when drawing 5 cards, we can use the concept of complementary probability. The complementary probability is the probability of the event not happening. In this case, it is the probability of not drawing any aces.

The total number of ways to draw 5 cards from a deck of 36 cards is given by the combination formula:

$$n = C_{36}^5$$

The number of ways to draw 5 cards without any aces is given by the combination formula:

$$m_0 = C_{27}^5$$

The number of ways to draw 5 cards with at least one ace is the complement of drawing 5 cards without any aces:

$$m_1 = n - m_0$$

The probability of not drawing any aces is:

$$P(\bar{A}) = \frac{m_0}{n}$$

The probability of drawing at least one ace is the complement of the probability of not drawing any aces:

$$P(A) = 1 - P(\bar{A})$$

Let's calculate the probabilities:

$$P(\bar{A}) = \frac{C_{27}^5}{C_{36}^5}$$

$$P(A) = 1 - P(\bar{A})$$

Using the combination formula, we can calculate the probabilities.

The probability of drawing at least one ace from a deck of 36 cards when drawing 5 cards is approximately 0.475.