Question

Из урны , содержащей 2 белых и 3 черных шара, наудачу извлекают 2 шара и добавляют 1 белый шар.Найти вероятность , что после этого наудачу выбранный из урны шар окажется белым.

Answer 1

2+3=5
5:2=2.5-вероятность

Answer 2

Calculating the Probability

To calculate the probability that a randomly chosen ball from the urn will be white after the described process, we can follow these steps:

1. Initial Probability Calculation: - Calculate the probability of drawing two balls and adding one white ball.

2. Final Probability Calculation: - Calculate the probability of drawing a white ball after the described process.

Let's proceed with the calculations.

Initial Probability Calculation

The initial probability can be calculated using the hypergeometric distribution formula, which is used to calculate the probability of drawing a specific number of successes (white balls) in a specific number of draws, without replacement.

The formula for the hypergeometric distribution is:

\[ P(X = k) = \frac{{\binom{K}{k} \cdot \binom{N - K}{n - k}}}{{\binom{N}{n}}} \]

Where: - \(N\) = total number of balls in the urn after adding one white ball - \(K\) = total number of white balls in the urn after adding one white ball - \(n\) = total number of draws - \(k\) = number of white balls drawn

Let's calculate the initial probability using the given information.

Final Probability Calculation

After adding one white ball, the total number of balls in the urn will change. We need to calculate the probability of drawing a white ball from the modified urn.

Let's proceed with the calculations to find the final probability.

Conclusion

By following the steps outlined above, we can calculate the probability of drawing a white ball from the urn after the described process.