Question

В урне лежат 9 пронумерованных шаров. Наугад берут 4 шара. Найти вероятность того, что среди взятых шаров 3 будут иметь четные номера ?

Answer 1

Probability of Drawing 3 Balls with Even Numbers

To find the probability of drawing 3 balls with even numbers out of 4 randomly selected balls from a urn containing 9 numbered balls, we need to calculate the ratio of the favorable outcomes to the total number of possible outcomes.

Let's break down the problem step by step:

1. Calculate the total number of possible outcomes: - We are drawing 4 balls from a total of 9 numbered balls, so the total number of possible outcomes is given by the combination formula: C(9, 4).

2. Calculate the number of favorable outcomes: - We want to draw 3 balls with even numbers. There are 4 even-numbered balls in the urn (2, 4, 6, 8), so the number of favorable outcomes is given by the combination formula: C(4, 3).

3. Calculate the probability: - The probability of drawing 3 balls with even numbers out of 4 randomly selected balls can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Let's calculate the probability using the formulas mentioned above:

1. Total number of possible outcomes: - C(9, 4) = 9! / (4! * (9-4)!) = 9! / (4! * 5!) = 9 * 8 * 7 * 6 / (4 * 3 * 2 * 1) = 126.

2. Number of favorable outcomes: - C(4, 3) = 4! / (3! * (4-3)!) = 4! / (3! * 1!) = 4.

3. Probability: - Probability = Number of favorable outcomes / Total number of possible outcomes = 4 / 126 ≈ 0.0317.

Therefore, the probability of drawing 3 balls with even numbers out of 4 randomly selected balls is approximately 0.0317 or 3.17%.