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 Type Identification (Posted on 2013-01-15)
On a remote island, precisely one third of the natives are liars who always lie, precisely one third are the knights who always speak truthfully and the remaining one third are the knaves who strictly alternate between lying and telling the truth.

The chances of encountering any one of the three types of natives on the road on the island are the same.

If a traveler meets a native on the road each of two successive days, what is the probability that at least one of the two natives is a knave?

 No Solution Yet Submitted by K Sengupta Rating: 2.0000 (2 votes)

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 Same answer, 3rd method Comment 2 of 2 |
The probability of not meeting a knave on 1 day = 2/3
The probability of not meeting a knave on two successive days
= (2/3)^2 = 4/9.
Therefore, the probability of meeting a knave is 1 - 4/9 = 5/9

The probability of meeting a knave on at least one of n meetings
= 1 - (2/3)^n

 Posted by Steve Herman on 2013-01-15 18:16:05

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