Stage: 5 Challenge Level: 
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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.
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Given all this has happened, the probability of selecting a green ball from bag 2 is now 3/5, so how many green balls were there in bag 2 at the outset?
Index notation/Indices. Theoretical probability. Long problems. Pythagoras' theorem. Combining probabilities. Surds. Golden ratio. Conditional probability. Mathematical reasoning & proof. Quadratic equations.
Published September 1998.
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