According to Sociology of Education (Apr. 2014), compensatory advantage occurs when individuals from privileged backgrounds are less dependent on prior negative outcomes than individuals from disadvantaged families. The researcher applied this theory to educational success. Let St represent the event that a student is successfully promoted to the next grade level in year t, and let Ft represent the event that a student fails to be promoted to the next grade level in year t. Now consider two probabilities: P1 = the probability that a student is successfully promoted to the next grade level in year t + 1 given that the student was successfully promoted the previous year (i.e., in year t) and P2 = the probability that a student is successfully promoted to the next grade level in year t + 1 given that the student failed in the previous year. Compensatory advantage theory states that the difference between the two probabilities, P1 - P2, is greater for disadvantaged families (say, the lower-class L) than for privileged families (say, the upper-class U).
a. Write P1 as a conditional probability using symbols.
b. Write P2 as a conditional probability using symbols.
c. The tables on p. 157 give the grade promotion results (number of students) for both upper- and lower-class students at a particular school. Does the compensatory advantage theory hold at this school?