50 Red and 50 Green Balls Puzzle Solution

Well the trick in the puzzle is that you have to maximize the probability of picking the Red ball. Now we know that the probability of picking one jar from two will be 1/2. So in order to increase the probability we need to do such that the whenever one jar is picked it gives only red balls and keeping the probability of picking the red ball in second jar also high.

Normal Scenario.
Let's say we do it like this
Jar A - 50 Red Balls
Jar B - 50 Green Balls

So Probability will be 0.5*1 + 0.5*0 = 0.5

But we are not getting any number from jar B as there is no Red Ball. So to increase the chances we do like this.

Jar A - 1 Red Ball
Jar B - 49 Red Balls and 50 Green Balls

So Probability will be 0.5*1 + 0.5 * (49/99) = 74/99.

So the maximum probability will be 74/99 of picking the red ball from a random jar.