Question

Имеются две урны: в первой 3 белых шара и 2 черных шара, во второй 4 белых и 4 черных шара. Из первой урны во вторую перекладывают не глядя,один шар. После этого из второй урны берут два шара. Найти вероятность того,что шары белые?

Answer 1

Ответ:

Из первой урны берут 2·3/(3+2) = 1.2 шара и перекладывают во вторую урну.

Там стало 5.2 белого шара из 10

Вероятность вытащить белый шар

P = 5.2/10 = 0.52

Answer 2

Probability of Drawing White Balls from Urns

To find the probability of drawing white balls from the second urn after transferring one ball from the first urn, we can calculate it step by step.

1. Total Number of Balls in the Second Urn: - After transferring one ball from the first urn to the second urn, the total number of balls in the second urn is 7.

2. Number of White Balls in the Second Urn: - The second urn initially had 4 white balls. After transferring one ball from the first urn, the number of white balls in the second urn could be 4 or 5, depending on the color of the transferred ball.

3. Probability Calculation: - If a white ball is transferred from the first urn to the second urn, the probability of drawing two white balls from the second urn would be calculated as the probability of drawing a white ball from the second urn multiplied by the probability of drawing another white ball from the second urn. - If a black ball is transferred from the first urn to the second urn, the probability of drawing two white balls from the second urn would be calculated as the probability of drawing a white ball from the second urn multiplied by the probability of drawing a black ball from the second urn.

4. Final Probability: - We can sum the probabilities calculated in the previous step to find the total probability of drawing two white balls from the second urn after the transfer.

Let's calculate the probability based on the above steps.