STAT 36217, HW 3, due Thursday 09/17/2009, 10:30 AM
1. Suppose that we have
n
coins such that if the
i
th
coin is flipped, heads will appear with
probability
i/n
,
i
= 1
,
2
, . . . , n
. When one of the coins is randomly selected and flipped,
it shows heads. Find an expression (involving
n
and
k
) for the probability that it was
the
k
th
coin (where 1
≤
k
≤
n
) (you may need the fact that 1+2+
. . .
+
n
=
n
(
n
+1)
/
2).
2. (
Three prisoners.
) Three prisoners, Antonio, Beppe and Carlo are on death row. The
governor decides to pardon one of them, randomly chosen. He informs the warden of
his choice but instructs him to keep the name of the pardoned prisoner secret. The
next day, Antonio, who, incidentally, never took 36217, tries to get the warden to tell
him who had been pardoned. The warden refuses. Antonio then asks which of Beppe
or Carlo will be executed. The warden thinks for a while and tries to remember what
he had learned in 36217, then tells Antonio that Beppe is to be executed.
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 Fall '09
 Jin
 Probability, Probability theory, Randomness, Beppe

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