Put out

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?

Problem

 

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Put Out

There are 5 yellow balls in bag 1. One ball is transferred to bag 2 which contains an unknown number of green balls.

 

Bag 2 is then shaken and a ball is selected at random and transferred to bag 1 without seeing its colour.

 

Bag 1 is then shaken and a ball is selected at random and transferred to bag 2 without seeing its colour.

 

Finally, a ball is chosen at random from bag 2.

 

If I tell you before you carry out this process that there's a $\frac{3}{5}$ chance you will end up with a green ball at the end, can you work out how many green balls are in bag 2 at the start?