# Probability Puzzle

• Jul 18th 2007, 12:19 PM
kens
Probability Puzzle
There are 50 red and 50 blue balls. Arrange them in 2 baskets, such that the probability of getting a blue ball is more.

• Jul 18th 2007, 12:27 PM
CaptainBlack
Quote:

Originally Posted by kens
There are 50 red and 50 blue balls. Arrange them in 2 baskets, such that the probability of getting a blue ball is more.

I think I need more detail for this

RonL
• Jul 18th 2007, 12:40 PM
kens
There are two baskets and we can put any number(even zero) balls in each of them.

I guess we can assume that x blue balls should be put in the first basket which has a total of n balls.
Then, we maximize
x/n +(50-x)/(100-n).

Is this correct? What is the answer?
• Jul 18th 2007, 12:42 PM
Soroban
Hello, kens!

Quote:

There are 50 red and 50 blue balls.
Arrange them in 2 baskets, such that the probability of getting a blue ball is a maximum.

This is a classic problem/puzzle/riddle.

Drag your cursor over the region between the asterisks.

* Place one blue ball in one basket, the rest in the other basket.

The probability of getting a blue ball from Basket #1 is: 1

The probability of getting a blue ball from Basker #2 is: 49/99

P(Basket 1 and blue) = (1/2)(1) = 1/2

P(Basket 2 and blue) = (1/2)(49/99) = 49/198

Therefore: P(blue) = 1/2 + 49/198 = 148/198 ≈ 75%
*

• Jul 18th 2007, 01:05 PM
kens
Thanks. Can you please suggest some books for such puzzles?