Optimize red-ball draw probability, prove optimality
Overview
This question evaluates probabilistic reasoning, optimization and mathematical proof skills by asking how to allocate red and blue balls across two boxes to maximize the probability of drawing a red, testing understanding of probability theory, combinatorics and constrained optimization.
Thumbtack
Oct 13, 2025, 9:49 PM
Data Scientist
Onsite
Statistics & Math
0
0
Loading...
Two-Box Ball Allocation to Maximize Probability of Drawing Red
Setup
- You have 2 boxes and two colors of balls.
- In the 100/100 case: 100 red and 100 blue balls.
- A box is chosen uniformly at random (probability 1/2 each), then one ball is drawn uniformly from that box.
Tasks
- For 100 red and 100 blue balls, how should you distribute the balls between the two boxes to maximize the probability of drawing a red ball? Compute the resulting probability.
- Prove optimality (not just intuition).
- Generalize: For R red and B blue balls (R,B ≥ 1), characterize the optimal allocation and give the maximal probability as a function of R and B.
Solution
Login required
Show