Each of Abner, Berenice, Calvin and Dolores is either a knight who always tells the truth, or a liar who always speaks falsely, or a knave who alternates between lying and telling the truth in any order.
They say:
- Abner: Berenice is a liar.
- Berenice: I am a knight.
- Calvin: If asked, Berenice would say that she is a knight.
- Dolores: I am a knight.
Given that each of the four individuals being any of the 3 types is equally likely, and all the four statements are simultaneous and independent, determine the probability that:
- Abner is a knight, Berenice is a liar and each of Calvin and Dolores is a knight.
*** For an extra challenge, solve this puzzle without taking resort to a computer program/excel solver aided methodology.
(In reply to
Extra Challenge Accepted (spoiler) by Steve Herman)
(1/2)*(2/3)*(2/3)*(2/5)=8/90=4/45=0.0888888888...
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Posted by Math Man
on 2023-09-12 17:51:06 |
re: Extra Challenge Accepted (spoiler)
