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The two Parrots
Christine inherits two indistinguishable parrots from her aunt. Christine would
prefer to have a pair (male and female) but has no idea what the birds are.
Assuming that its equally likely that a bird is a male or a female the
probability of having a pair is 50%.
After a while one of the parrots gets
sick and Christine takes the parrot to a doctor. The
doctor tells her that the parrot is a male. As the
other one could still be either male or female the probability
of a pair is still at 50%.
Some weeks pass, and a parrot gets sick again. As Christine cannot
distinguish the two parrots she does not know if the same
one got ill or the other one. She takes the sick bird to the
doctor and he tells her that this bird is a male.
Hint: assume that the visits to the doctor continue many
times, and each time the doctor claims that the ill bird is
a male.
I heard this problem only once in a probability class
and unfortunately our teacher never told us where he got it from.
If you know a reference please let me know.
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