Question

Задача: В урне 5 белых, 8 синих и 7 красных шаров.Найдите вероятность того, что наудачу извлеченный из урны шар окажется: 1)белым 2)красным 3)синим 4)белым и синим 5)белым и красным 5)цветным. Помогите пожалуйста решить задачу, мне нужно подробное решение

Answer 1

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Всего 10 шаров

Answer 2

Всего шаров 10 .
вероятность того,что шар цветной : 8/10 или 0,8

Answer 3

Probability of Drawing Different Colored Balls from an Urn

To find the probability of drawing different colored balls from the urn, we can use the formula for probability:

1) Probability of drawing a white ball: - Given: 5 white, 8 blue, and 7 red balls in the urn. - Using the formula for probability: - $P(\text{white}) = \frac{C_{5}^1 \cdot C_{15}^{1}}{C_{20}^2}$ - Substituting the values: - $P(\text{white}) = \frac{5 \cdot 15}{190} = \frac{3}{38} \approx 0.079$

2) Probability of drawing a red ball: - Using the same formula for probability: - $P(\text{red}) = \frac{C_{7}^1 \cdot C_{13}^{1}}{C_{20}^2}$ - Substituting the values: - $P(\text{red}) = \frac{7 \cdot 13}{190} = \frac{91}{190} \approx 0.479$

3) Probability of drawing a blue ball: - Similarly, using the formula for probability: - $P(\text{blue}) = \frac{C_{8}^1 \cdot C_{12}^{1}}{C_{20}^2}$ - Substituting the values: - $P(\text{blue}) = \frac{8 \cdot 12}{190} = \frac{24}{95} \approx 0.253$

4) Probability of drawing a white and a blue ball: - Using the formula for probability: - $P(\text{white and blue}) = \frac{C_{5}^1 \cdot C_{8}^{1}}{C_{20}^2}$ - Substituting the values: - $P(\text{white and blue}) = \frac{5 \cdot 8}{190} = \frac{2}{19} \approx 0.105$

5) Probability of drawing a white and a red ball: - Using the formula for probability: - $P(\text{white and red}) = \frac{C_{5}^1 \cdot C_{7}^{1}}{C_{20}^2}$ - Substituting the values: - $P(\text{white and red}) = \frac{5 \cdot 7}{190} = \frac{7}{38} \approx 0.184$

6) Probability of drawing balls of any color: - The probability of drawing a ball of any color is 1, as it is certain that a ball will be drawn from the urn.

These calculations provide the probabilities for each scenario based on the given numbers of balls in the urn.