Island's Ritual

Probability Level 1

In an Island total of $1001$ people lived out of which $500$ were Knight, $500$ were Knaves and $1$ was Joker.

On Opposite Day there is a ritual that everyone will say opposite of what they want to tell to the person they are communicating with. (everyone obey this)

Once you visited the Island and someone told you "Today, is Opposite Day", is the probability that the person is not a Knight is $P$ then find $\lfloor 10^2 P\rfloor$

Details :

On normal circumstances if Knight tells $A$ then $A$ is true, If Knave tells $A$ then $\neg A$ is true, and if the Joker tells $A$ then either $A$ or $\neg A$ is true
On Opposite Day if someone tells you $A$ then what they are telling you is $\neg A$

The answer is 100.

1 solution

A Former Brilliant Member
Mar 21, 2021

A knight will always tell the truth, except on opposite day, when the knight will lie. Let us say the person we meet is a knight. Then he must be lying when he says 'Today, is Opposite Day', but today is opposite day, which leads to a contradiction. This means the person can't be a knight. So the probability that the person is not a knight, $P = 1$ .

$\left \lfloor10^{2}(1) \right \rfloor = \boxed{100}$

Island's Ritual

The answer is 100.

1 solution

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