Suppose that we have a data set of doctoral students in economics. This data set includes whether each student had a major in economics from his or her undergraduate institution and whether the same student earned a master's degree before starting a PhD program. Also, this data set includes information on which subfield of economics the student is interested in. Let's define the events E, M, FMicro, FMacro, and FMetrics as follows: E = {Economics major} M = {Having a master degree} FMicro = {Choosing microeconomics as a sub-field} FMacro = {Choosing macroeconomics as a sub-field} FMetrics = {Choosing econometrics as a sub-field}   FMicro FMacro FMetrics Total E∩M .150 .150 .100 .400 E∩MC .050 .075 .050 .175 EC∩M .050 .100 .050 .200 EC∩MC .050 .150 .025 .225 Total .300 .475 .225     1) Suppose we learn that a student got a major in economics. What probability should we assing to the event that this student does NOT have a master's degree? 2) Suppose we learn that a student has a master's degree. What probability should we assign to the even that this student had a major in economics and chooses either Macroeconomics or Econometrics as a sub-field? 3) Suppose we learn that a student chooses Microeconomics as a sub-field. What probability should we assign to the event that this student was NOT a major in economics?

Suppose that we have a data set of doctoral students in economics. This data set includes whether each student had a major in economics from his or her undergraduate institution and whether the same student earned a master's degree before starting a PhD program. Also, this data set includes information on which subfield of economics the student is interested in. Let's define the events E, M, F_Micro, F_Macro, and F_Metrics as follows:

E = {Economics major}

M = {Having a master degree}

F_Micro = {Choosing microeconomics as a sub-field}

F_Macro = {Choosing macroeconomics as a sub-field}

F_Metrics = {Choosing econometrics as a sub-field}

1) Suppose we learn that a student got a major in economics. What probability should we assing to the event that this student does NOT have a master's degree?

2) Suppose we learn that a student has a master's degree. What probability should we assign to the even that this student had a major in economics and chooses either Macroeconomics or Econometrics as a sub-field?

3) Suppose we learn that a student chooses Microeconomics as a sub-field. What probability should we assign to the event that this student was NOT a major in economics?