Question

В урне 4 белых шара и 10 черных. Из урны наугад извлекают 3 шара. Найдите вероятность того, что они один шар белый и два черных

Answer 1

Рассмотрите такой вариант:
$P= \frac{C^1_4*C^2_{10}}{C^3_{14}}$
Отсюда вероятность равна 45/91.
Пояснение: общее число всевозможных исходов есть сочетания из 14 по 3. Нужное количество исходов есть произведение (правило "И") сочетаний из 4 по 1 (один белый шар) на число сочетаний из 10 по 2 (чёрные шары, два).

Answer 2

Probability Calculation for Drawing 3 Balls from an Urn

To find the probability of drawing one white ball and two black balls from the urn, we can use the formula for calculating probabilities in such scenarios.

The formula for the probability of an event is given by:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

In this case, the number of favorable outcomes is the number of ways to choose 1 white ball out of 4 and 2 black balls out of 10. The total number of possible outcomes is the number of ways to choose 3 balls out of the total 14 balls.

Calculation

Using the formula, the probability can be calculated as follows:

Number of favorable outcomes: - Choosing 1 white ball out of 4: C(4, 1) = 4 - Choosing 2 black balls out of 10: C(10, 2) = 45 - Total favorable outcomes: 4 * 45 = 180

Total number of possible outcomes: - Choosing 3 balls out of 14: C(14, 3) = 364

Probability: - Probability = 180 / 364 ≈ 0.4945

Therefore, the probability of drawing one white ball and two black balls from the urn is approximately 0.4945.

(#1)