Question

В коробке находятся 18 белых, 12 зеленых, 20 красных шаров. Наугад извлечено 7 шаров. Какова вероятность того, что вынутыми шарами будут 2 белых и 1 зелёный?

Answer 1

Условие: извлечено 7 шаров +сумма беллых и зелёных

Получим P(A)=N(A)/N=3/30=0.1

 

 

 

Answer 2

Problem Analysis

We are given a box containing 18 white, 12 green, and 20 red balls. We need to find the probability of drawing 2 white balls and 1 green ball out of 7 randomly drawn balls.

Solution

To find the probability, we need to calculate the total number of favorable outcomes and divide it by the total number of possible outcomes.

The total number of possible outcomes is the number of ways we can choose 7 balls out of the total number of balls in the box, which is 50.

The total number of favorable outcomes is the number of ways we can choose 2 white balls out of 18 and 1 green ball out of 12.

Let's calculate the probability step by step:

Step 1: Calculate the number of ways to choose 2 white balls out of 18. This can be calculated using the combination formula: C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to be chosen.

Using this formula, the number of ways to choose 2 white balls out of 18 is: C(18, 2) = 18! / (2!(18-2)!) = 18! / (2!16!) = (18 * 17) / (2 * 1) = 153.

Step 2: Calculate the number of ways to choose 1 green ball out of 12. Using the same combination formula, the number of ways to choose 1 green ball out of 12 is: C(12, 1) = 12! / (1!(12-1)!) = 12! / (1!11!) = 12.

Step 3: Calculate the total number of favorable outcomes. The total number of favorable outcomes is the product of the number of ways to choose 2 white balls and 1 green ball: Total favorable outcomes = C(18, 2) * C(12, 1) = 153 * 12 = 1836.

Step 4: Calculate the total number of possible outcomes. The total number of possible outcomes is the number of ways to choose 7 balls out of 50: Total possible outcomes = C(50, 7) = 50! / (7!(50-7)!) = 50! / (7!43!) = 50 * 49 * 48 * 47 * 46 * 45 * 44 / (7 * 6 * 5 * 4 * 3 * 2 * 1) = 99,884,400.

Step 5: Calculate the probability. The probability of drawing 2 white balls and 1 green ball out of 7 randomly drawn balls is the ratio of the total number of favorable outcomes to the total number of possible outcomes: Probability = Total favorable outcomes / Total possible outcomes = 1836 / 99,884,400.

Now, let's calculate the probability:

Probability = 1836 / 99,884,400 ≈ 0.0000184.

Therefore, the probability of drawing 2 white balls and 1 green ball out of 7 randomly drawn balls is approximately 0.0000184.

Answer

The probability of drawing 2 white balls and 1 green ball out of 7 randomly drawn balls is approximately 0.0000184.