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, 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
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?
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