The chance that somebody get's mad cow disease is 0.01 (1%). If someone visits the USA this chance becomes 0.05 (5%). The chance that somebody goes to the USA is 0.01 (1%). If someone goes to the USA, he'll most likely buy the flag as a souvenir, the chance that somebody does this is 0.7 (70%). Because the flag is well known, people who never have been to the USA have a chance of 0.3 (30%) to have the flag. Now given that somebody has the mad cow disease and he has the flag of the USA, what are the chances he has visited the USA?
P(USA) = 0.01
P(MCD) = 0.01
P(MCD|USA) = 0.05
P(flag|!USA) = 0.3
P(flag|USA) = 0.7
Following bayes' rule we can calculate the chance that somebody has been to america given the knowledge this person has MCD:
P(USA|MCD) = P(MCD|USA)*P(USA)/P(MCD) = 0.05 *0.01 / 0.01 = 0.05.
Now the problem is how do we calculate the chance that someone has visited the USA given he has the american flag, and after that given somebody has and mad cow disease and the american flag the chance he has been to america.
How does one does this?