2) A poll of citizens of a certain country asked whether or not they approve of the three political parties. The results show that 49% of respondents approve of party A, 47% approve of party B, and 19% approve of party C. The results also show that 2% of respondents approve of all three parties, 5% of respondents approve of both party A and party B, 13% of respondents approve of both party A and party C, and 2% of respondents approve of both party B and party C.
a) Draw a Venn diagram to represent this data. Let A be the event that a respondent approves of party A, B be the event that a respondent approves of party B, and C be the event that a respondent approves of party C.
b) Calculate $P[B \cap C]$
c) Calculate $P[A \cup B]$
d) Calculate $P[A^c \cup B^c]$
e) Calculate $P[A^c \cup B \cup C^c]$
f) Calculate $P[A^c \cap B^c \cap C^c]$
g) Calculate $P[C^c \cup B]$
h) Calculate $P[A \cap (B \cup C^c)]$
i) Calculate $P[A|B]$
j) Calculate $P[C^c|B^c]$