Who Attends Chicago Public Schools? A Breakdown by Race

While Chicagoans understand that white students are less likely to enroll in CPS schools than students of color, few seem to know how big the difference is.  Using Bayes' formula and publicly available data (located here, here, and here), I calculated the probability that a Chicago child of African American, Hispanic, Asian, white, and multi-racial descent attends the public schools.  Here are the results:

5-19 year olds in ChicagoPr(attends CPS)Pr(race)Pr(race | attends CPS)Pr(attends CPS | race)
Hispanic0.79710.4000.4520.90
African American0.79710.3900.3970.81
Asian0.79710.0360.0350.78
Multi-Racial0.79710.0170.0110.52
White0.79710.1550.0920.47

Pr(attends CPS) is the probability that a child (between 5 and 19 years old) in Chicago attends a public school.  Pr(race) is the probability that a randomly chosen child in Chicago belongs to a given race; for example, the probability that a Chicago child is white is 15.5%.  Pr(race | attends CPS) is the probability that a randomly chosen CPS student is a given race; for example, about 39.7% of CPS students are African American.

From these three inputs, I calculate Pr(attend CPS | race), the probability that a child of a given race attends a Chicago public school.  While nine in ten Hispanic children and eight in ten African American children in Chicago are enrolled in CPS, fewer than five in ten white children are.  An African American student is 1.7 times more likely to attend a CPS school than a white student.  An Hispanic student is almost twice as likely.