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.

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional