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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.

Is the probability that Christine has a male and female still at 50%?

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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