Tuesday, May 29, 2007

For probability afficionados.

Given N Red and N Blue balls, arrange all the balls in 2 baskets, such that given the event of a blind-folded person selecting a random ball from a random basket, the probability of getting a Blue ball is > 0.5.

I couldn't think of an answer, but there is a clever answer suggested by one of my colleagues.See the comment.


sudeep said...

Vivek wrote:

Seems to me the best way is to put one blue ball in one basket and all the rest in the other - this way the probability is
.5 + .5*(n-1)/2n. Best case situation would be .75 for very large n. Just an intuitive answer - would be interesting to look for a proper proof.

With Regards,

Sudeep wrote:

Oh, good approach.....

So Generically can we say :-
Reqd. Probability = 0.5 * [ sum of two fractions ].

If we ensure that the sum of two fractions is > 1 (like the one Vivek has shown), we can say that the probability of getting a blue ball is higher than 0.5.

i.e. :-

Keep x blue balls in Bag1 , where x > 1 and x < N
Keep (N-x) blue balls in Bag2 and all the N Red balls in Bag2.

We need to find that x, such that we get the highest probability.


Anonymous said...

Question was about a random ball from a random bucket right?. Is it possible to keep fraction greater than 1 on BOTH the Baskets.... Anyone know Braille??..

Tejaswi said...

1 ball in bag_A is good enough to ensure a blue ball if bag_A is picked. The remaining N-1 blue balls will try to maximize blue balls' odds in bag_B, where they have N red balls to contend with. This is the optimal solution because to increase the odds of picking up a blue ball amidst red and blue balls, we need as many blue balls as possible, and that's N-1.

But why would he want blue balls, is my question. I can agree with wanting the Blue Pill, but blue balls!?!?!


sudeep said...

Blue balls or blue pills....I am in a red pill mood today....

How abt red berries and blue berries.

That would be a motivation for the Blind man

Life is sometimes as trivial as a blue pill and sometimes like a piece of complex &*%^&* like a red pill....