A bag contains 8 balls, whose colours are either white or black.

Question

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and 2 are found to be white and 2 black. The probability that the bag contains equal numbers of white and black balls is:

Accepted Answer

Using Bayes' theorem over equally-likely compositions (from 2W-6B up to 6W-2B) and computing the likelihood of drawing 2W-2B for each, the composition 4W-4B gives the highest weight, and normalizing yields

$$P(4W,4B\mid 2W,2B\text{ drawn}) = \frac27$$

Solutions · 1