Question

В первой урне 2 белых и 3 черных шара. Во второй урне 3 белых.Из каждой удалили по одному наугад взятому шару, а оставшиеся шары поместили в третью урну. какова вероятность события А - шар, взятый наугад из 3-й урны, белый?

Answer 1

2/5*1/2+3/5*2/3=1/5+2/5=3/5=0,6=60%

Answer 2

Probability of Drawing a White Ball from the Third Urn

To calculate the probability of drawing a white ball from the third urn, we can use the concept of conditional probability. Let's break down the steps to find the probability of this event.

1. Initial Ball Distribution: - First urn: 2 white balls and 3 black balls. - Second urn: 3 white balls.

2. Random Removal and Transfer: - One ball is removed at random from each urn. - The remaining balls are placed in the third urn.

3. Calculating the Probability: - We need to find the probability of drawing a white ball from the third urn after the transfer.

Conditional Probability Calculation

The probability of drawing a white ball from the third urn can be calculated using the formula for conditional probability:

P(A|B) = P(A ∩ B) / P(B)

Where: - P(A|B) is the probability of event A given event B. - P(A ∩ B) is the probability of both events A and B occurring. - P(B) is the probability of event B occurring.

Applying the Formula

In this scenario: - Event A: Drawing a white ball from the third urn. - Event B: The specific combination of balls transferred to the third urn.

We need to calculate the probabilities of these events and apply the formula to find the desired probability.

Conclusion

By applying the concept of conditional probability, we can determine the likelihood of drawing a white ball from the third urn after the random transfer of balls from the first and second urns.