Practice FT3 Q9 - Looking for a detailed, worked solution with theoretical explanation

Two political parties, one called Team Theory and the other called Polemic Party are competing in an election. When polled, 45.04% of voters reported their intention to vote for Polemic Party, while 54.93% reported that they will vote for Team Theory. However, these values are not accurate, because some of the voters tied in the poll. It is known that 4% of Team Theory supporters are liars {if asked, they say they support Polemic Party], and that 2% of Polemic Party are liars {they claim that they support Team Theory}. a} Let p be the probability that a voter selected at random is a supporter of Polemic Party, and let g be the probability that a randomly selected Polemic Party supporter [someone who intends to vote for Polemic Party] is a liar. Express the probability that a person is both a liar and a Polemic Party supporter in terms of p and {1. Probability that a voter is both a liar and a Polemic Party supporter = I n. IE b} Let r be the probability that a Team Theory supporter is a liar. Express the probability that a voter selected at random is both a Team Theory supporter and not a liar in terms otp and 1". Probability that a person is not a liar and is a Team Theory supporter = I n .I c} Using the calculations above [or otherwise]: nd the percentage of voters who actually intend to vote for Polemic Party and type it in the box below. Percentage = I n IE '34:. Do not include the \"a\": sign in your