You are blindfolded and placed in front a table with two jars. One jar has $50$ red balls and other has $50$ blue balls.
What should be your strategy so that you pick up the red ball with more than $50\%$ probability.
You are blindfolded and placed in front a table with two jars. One jar has $50$ red balls and other has $50$ blue balls.
What should be your strategy so that you pick up the red ball with more than $50\%$ probability.
Take one ball from each jar. You're guaranteed to get a red.
If the red and blue balls are identical in shape and size and picking one ball from two jars which are also identical should result in the probability of getting a red ball as .5. Now if the experiment is biased in some way, then the probability of getting a red ball may be greatr than .5.
I don't think moving the balls makes any difference.
The question is what is your strategy to improve from 50% of the balls. Not 50% out of one jar.
Ultimately there are always 100 balls in front of you and you have a 50/50 chance. The only way to change that is to take two balls out, or throw away one balls so that N changes.
take 49 red balls from one jar and put them in the other jar wit the blue balls,
now its 100 % he will pick red from the first jar, and 50% red from the mixed jar.