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Put Out

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

bags
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?