Maximize Probability of Drawing Two Red Balls

Q: Maximize Probability of Drawing Two Red Balls

This question evaluates probability theory, combinatorial reasoning, and constrained optimization skills by requiring allocation of discrete items to maximize the probability of a joint event.

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Question

Optimize Two-Basket Allocation for Red-Red Draws

Setup

You have 100 red balls and 100 blue balls to distribute between two baskets, A and B. Then you will draw one ball from each basket (no replacement within a basket, but since only one draw is made per basket, replacement is irrelevant).

Task

How should you allocate the balls between the two baskets to maximize the probability that both drawn balls are red? Compute that maximum probability.

Notation Hint

Let x = number of red balls in basket A.
Let u = number of blue balls in basket A.
Then basket B has (100 − x) red and (100 − u) blue.
The goal is to maximize P(red from A) × P(red from B).

Maximize Probability of Drawing Two Red Balls

Optimize Two-Basket Allocation for Red-Red Draws

Setup

Task

Notation Hint

Solution

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