Everybody in Ourtown is a fool or a knave or possibly both. 70% of the citizens are fools and 85% are knaves. One citizen is randomly select

Question

Everybody in Ourtown is a fool or a knave or possibly both. 70% of the citizens are fools and 85% are knaves. One citizen is randomly selected to be mayor. What is the probability that the mayor is both a fool and a knave?

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2 weeks 2022-01-12T16:02:45+00:00 1 Answer 0 views 0

There is a 55% probability that the mayor is both a fool and a knave.

Step-by-step explanation:

We solve this problem building the Venn’s diagram of these probabilities.

I am going to say that:

A is the probability that someone in Ourtown is a fool.

B is the probability that someone in Ourtown is a knave.

We have that: In which a is the probability that someone in ourtown is a fool but not a knave and is the probability that someone in Ourtown is both these things

By the same logic, we have that: Everybody in Ourtown is a fool or a knave or possibly both.

This means that the union of these sets is 1, that is, In which So 70% of the citizens are fools

This means that    85% are knaves

This means that    What is the probability that the mayor is both a fool and a knave?

A mayor is a random citizen just like any other, so this probability is the same as it would be for any person.

This is , which we can find replacing both a and b in the equation below.    There is a 55% probability that the mayor is both a fool and a knave.