Question

Suppose there are 10 black quarterbacks and 25 white quarterbacks in the NFL draft, and that all quarterbacks are of equal ability; specifically, all quarterbacks in the draft have a 20% chance of succeeding in the NFL. However, suppose NFL coaches have an incorrect view that white quarterbacks are more likely to succeed than black quarterbacks. As a result, they decide to cut ½ of all black quarterbacks that were drafted and ¹/₅ of all white quarterbacks that were drafted.

a) How many of the white quarterbacks that survived the initial cuts will be successful? [1st blank]

b) How many of the black quarterbacks that survived the initial cuts will be successful? [2nd blank]

c) Of the 25 white quarterbacks in the NFL draft, what percentage will survive the cuts and be successful? [3rd blank]

d) Of the 10 black quarterbacks in the NFL draft, what percentage will survive the cuts and be successful? [4th blank]

e) Are NFL coaches likely to think that cutting ½ of all black quarterbacks and ¹/₅ of all white quarterbacks is a smart idea? [5th blank: write "yes" or "no"]

f) Is this type of discrimination likely to persist or disappear over time? [6th blank: write "yes" or "no"]

Answer 1

There are 10 black quarterbacks and 25 white quarterbacks. All are of equal ability. All quarterbacks in the draft meaning 25+10 = 35 have a 20% chance of succeeding in the NFL.

However, NFL coaches think that white are more likely to succeed.

Thus, they cut 1/2 of all black quarterbacks: 10/2 = 5 are cut.

1/5 of white quarterbacks are cut = 25/5 = 5 are cut.

a) White quarterbacks which survived the initial cut are 20. Thus all have 20% chance. 20*0.2 = 4 have a chance of being successful.

b) 5 black quarterbacks survive the initial cut and 5*0.2 = 1 has a chance of being successful.

c) Of the 25 white quarterbacks; 4/25 = 16% have a chance of surving the cut and being successful

d) Of the 10 black quarterbacks; 1/10= 10% have a chance of surviving the cut and being successful.

e) Yes, based on the figure that white are more likely to be successful as they have a 16% chance whereas blacks have only 10% chance of being successful.

f) This type of discrimination is likely to persist over time if no coherent action is taken to address such issues as these are merely chances and sports is a game of luck. Selecting the same number of blacks and whites will go a long way to address this sort of discrimination.