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Suppose that initially the jewels in P are worth (a + b + 5000),
and those in Q are worth (c + d + e).
The average value in P at the start is \frac {a + b + 5000}3
After the jewel has been moved it is \frac{a + b}2.
Therefore:
\begin{equation}
\frac {a + b + 5000}3 = \frac{a + b }{2} - 1000
\end{equation}
A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?
Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?
You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?