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Probability of getting a white marble:
If half the marbles in each box are white,
the probability that she wins her freedom is $\frac12$
Otherwise, one box will be more than $\frac12$ white and the other will be less than $\frac12$ white.
To maximise her probability of freedom we need to get as close to $1$ in one box and to $\frac12$ in the other box as possible. We do this by putting just one white marble in one box:
Probability of freedom is $\frac12\times(1+\frac9{19})=\frac{28}{38}$, which is nearly $74\%$.
Winning Marble
Age 14 to 16
ShortChallenge Level 
Probability of getting a white marble:
$\frac12\times(${proportion white in box 1} $+$ {proportion white in box 2}$)$
If half the marbles in each box are white,
the probability that she wins her freedom is $\frac12$
Otherwise, one box will be more than $\frac12$ white and the other will be less than $\frac12$ white.
To maximise her probability of freedom we need to get as close to $1$ in one box and to $\frac12$ in the other box as possible. We do this by putting just one white marble in one box:
Probability of freedom is $\frac12\times(1+\frac9{19})=\frac{28}{38}$, which is nearly $74\%$.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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