A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 are black. The probability that the bag contains equal number of white and black balls is:
Step-by-Step Solution
Key Concept: Use Bayes' theorem. The bag has 8 balls; possible compositions are $(W,B)\in\{(2,6),(3,5),(4,4),(5,3),(6,2)\}$ — each equally likely a priori. Compute $P(\text{draw 2W 2B}\mid\text{composition})$ for each, then apply Bayes.
Bayes: $P(4W4B|\text{obs})=\frac{36}{126}=\frac{2}{7}$.
Correct Answer: 2