1. The chart below shows results of a survey conducted shortly after the 2016 US Presidential election. The respondents in the bottom bar are those who are in one or both of the top two bars. About one in four report sharing fabricated newe whether aware at the time or not % of US. (\"I'M/fr Wm my May... Shared a political news story online - 16/ they later found out was made up Shared a political news story online - 140/ they knew at the time was made up Did either/both of these 23% Source: Survey conducted Dec. 1-4 2016. "Many Americans Believe Fake News is Sowing Confusion" PEW RESEARCH CENTER Suppose one person is picked at random from the survey respondents. Define the following events. . A: the person shared a political news story online they later found was made up. . B: the person shared a political news story online they knew at the time was made up. a) Find P(AB). b) Fill in the blank in the statement P(A | B) P(A) with one of the symbols . Justify your choice by calculating both the probabilities. c) Are A and B independent? Explain based on your calculations in the parts above. d) Find P(B\"A)