Question

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

Answer 1

Answer:

$P( F \cap K) =0.7+0.85 -1=0.55$

Step-by-step explanation:

For this case we can define some notation first:

F ="One person is fool "

K="One person is knave"

And we have the following probabilities given:

$P(F) = 0.7 , P(K) =0.85$

And from the given condition that everyone is fool or knave we can deduce that:

$P(K UF) =1$

Solution to the problem

For this case we want to find this probability:

$P( F \cap K)$

And we can use the total probability rule given by:

$P(K \cup F) = P(F) +P(K) -P(K \cap F)$

And replacing the values that we have we got:

$1 = 0.7+0.85 -P(K \cap F)$

And if we solve for $P( F \cap K)$ we got:

$P( F \cap K) =0.7+0.85 -1=0.55$