Question

В урне лежат 10 белых шаров и 11 рыжих шаров. Случайным образом достают 5 шаров. Какова вероятность того, что среди этих 5 шаров ровно 3 шара белых?

Answer 1

У меня такое получается - 1980/61047

Answer 2

Problem Analysis

We have an urn containing 10 white balls and 11 red balls. We randomly draw 5 balls from the urn. We need to find the probability of getting exactly 3 white balls out of the 5 drawn.

Solution

To find the probability, we need to calculate the number of favorable outcomes (getting exactly 3 white balls) and divide it by the total number of possible outcomes (drawing any 5 balls from the urn).

The number of favorable outcomes can be calculated by choosing 3 white balls out of the 10 available white balls and 2 balls out of the remaining 11 red balls. This can be calculated using the combination formula:

Number of favorable outcomes = C(10, 3) * C(11, 2)

The total number of possible outcomes is the number of ways to choose any 5 balls out of the total 21 balls in the urn:

Total number of possible outcomes = C(21, 5)

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

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

Let's calculate the probability.

Calculation

Using the combination formula, we can calculate the number of favorable outcomes and the total number of possible outcomes.

Number of favorable outcomes: C(10, 3) * C(11, 2) = 120 * 55 = 6600

Total number of possible outcomes: C(21, 5) = 20349

Probability: Probability = Number of favorable outcomes / Total number of possible outcomes = 6600 / 20349 ≈ 0.324

Therefore, the probability of getting exactly 3 white balls out of the 5 drawn is approximately 0.324.