Reverse statistics problem

Question

In a population of voters, 30% favour an election issue, and 70% do not favour it. In a survey it is
found that 40% of those who favour the issue vote for the ruling party, while 80% of those who do
not favour the issue vote for the ruling party.

A person chosen at random is found to be from the ruling party. What is the probability that the chosen person does not favour the election issue?

Answer 1

Let N = 1000 voters.

Based on the given info:

300 in favor

700 opposed

120 in favor, ruling party

56 opposed, ruling party

 

Now we can set up a table like this:

 

                                   IN FAVOR                  OPPOSED          TOTAL

 

Ruling party                   120                               56               176  

 

Non ruling party             180                               644             824    

------------------------------------------------------------------

Total                              300                               700

 

the grand total is in fact 1000 as expected

 

Probability that the voter from the ruling party is opposed is 56/176 = 28/88 = 14/44 = 7/22 = .318181818... 

                 or almost 32%