Question

Имеются три одинаковых урны. В первой 2 белых и 3 чёрных шара, во второй – 4 белых и 1 чёрный шар, в третьей – 3 белых шара. Экспериментатор подходит к одной из урн и вынимает шар. найти вероятность того, что это белый шар

Answer 1

Просто 9/13 так как всего шаров 13, а белых 9

Answer 2

Calculating the Probability of Drawing a White Ball

To calculate the probability of drawing a white ball, we can use the concept of conditional probability. Let's denote the events as follows: - A: The ball is drawn from the first urn. - B: The ball is drawn from the second urn. - C: The ball is drawn from the third urn. - W: The ball drawn is white.

We can then use the law of total probability to calculate the overall probability of drawing a white ball.

Probability Calculation

The probability of drawing a white ball can be calculated as follows:

1. Calculate the probability of drawing a white ball from each urn: - From the first urn: P(W|A) = 2/5 - From the second urn: P(W|B) = 4/5 - From the third urn: P(W|C) = 3/3 = 1

2. Calculate the overall probability of drawing a white ball using the law of total probability: - P(W) = P(W|A) * P(A) + P(W|B) * P(B) + P(W|C) * P(C) - P(A), P(B), and P(C) are the probabilities of drawing from each urn, which are equal since the experimentator chooses an urn at random. Therefore, P(A) = P(B) = P(C) = 1/3.

3. Substitute the values and calculate the overall probability: - P(W) = (2/5) * (1/3) + (4/5) * (1/3) + (1) * (1/3) - P(W) = 2/15 + 4/15 + 1/3 - P(W) = 2/15 + 4/15 + 5/15 - P(W) = 11/15

Conclusion

The probability of the experimenter drawing a white ball from any of the three urns is 11/15.