CareerCup

In bag1 place only one red ball and put all the remaining red and black balls on bag2.

prob: 1*0.5+49/99*0.5

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.