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

Please help.

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- Jul 18th 2007, 11:19 AMkensProbability 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.

Please help. - Jul 18th 2007, 11:27 AMCaptainBlack
- Jul 18th 2007, 11:40 AMkens
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, 11:42 AMSoroban
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.

I'll hide the answer.

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, 12:05 PMkens
Thanks. Can you please suggest some books for such puzzles?