Final answer:
The question involves calculating the expected number of black balls drawn without replacement from a box, a common problem in high school Mathematics probability. It requires an understanding of probabilities, expected values, and hypergeometric distribution.
Step-by-step explanation:
The question asks about the expected number of black balls drawn from a box without replacement, considering balls are drawn from another box as well. The question falls under the subject of probability in Mathematics, specifically concerning expected value calculations and the concept of drawing without replacement. To calculate this, one should understand the weighted average and the use of probabilities in such complex scenarios. It involves calculating the probability of drawing a black ball from each box and then using these probabilities to find the expected number of black balls drawn. Often, these types of problems require knowledge of the hypergeometric distribution, which is applicable when dealing with samples drawn without replacement from a finite population.
An approach to solve a simpler version of this problem is given by an example where the total number of outcomes and the favorable outcomes are used to calculate probabilities. Events that are mutually exclusive and independent are also considered in such probability questions. The detailed answer provided would help a student in high school studying probability, which is often covered in courses dealing with advanced placement (AP) statistics or high school mathematics.