There are 14 blue and 14 red balls in your pocket. You take

Question

There are 14 blue and 14 red balls in your pocket. You take two of them out of your pocket at the same time. If they are of the same color you add a blue ball. If they are of different colors you add a red ball. What will be the color of the last ball in your pocket?

twixt · Answer

Is this an official stem ?

This problem is symmetric as blue and red balls are equally weighted.
I do not understand the question. Maybe something like (what is the prob to pick a blue as last ball ?) sounds better, then the answer should be 1/2 to me...

hardworker_indian · Answer

I think Blue.

But I am wondering about the number 14. Also, as red ball decreases the pb of picking red balls together decreases.

boksana · Answer

Don't you think that it would be easier to find out color by using probability?
P(blue, blue)=13/54
P(red, red)=13/54
P(same color)=13/27
P(blue, red)=P(red, blue)=18/27

so I guess it's red.
Correct me if I'm wrong :roll:

Dharmin · Answer

It is recurssive function.
The answer is blue - regardless of picking orders and regardless of picking different color balls or picking same color balls.


Solution:
(1) Picking same color balls everytime:

(Picking of 28 balls will take 14 operations and as everytime they are of same color)

Iteration - 1 will complete with : 14 blue balls
Iteration - 2 will complete with : 7 blue balls
Iteration - 3 will complete with : 3 + 1(left from last action)
Iteration - 4 will complete with : 2 Blue balls
Iteration - 5 will complete with : 1 Blue ball

(2) Picking different color balls everytime: (i.e. 1 red and 1 blue)

Iteration - 1 will complete with : 14 RED balls 
(now it will follow the same pattern bcoz all balls are of same color)
Iteration - 2 will complete with : 7 blue balls
Iteration - 3 will complete with : 3 + 1(left from last action)
Iteration - 4 will complete with : 2 Blue balls
Iteration - 5 will complete with : 1 Blue ball

cheers,
Dharmin

There are 14 blue and 14 red balls in your pocket. You take

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