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?

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.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

true

step-by-step explanation:

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