Chapter 3.6, Problem 50E

The information in Exercise $49$ is rather dated. Use the following to determine whether things have improved since then. In April $2003$, Amnesty International issued a study on race and death penalty. The following quote is from that study:

“The population of the USA is approximately $75$ percent white and $12$ percent black. Since $1976$, blacks have been six to seven times more likely to be murdered than whites, with the result that blacks and whites of murder in about equal numbers. Yet, $80$ percent of the more than $840$ people put to death in the USA since $1976$ were convicted of crimes involving white victims, compared to the 13 percent who were convicted of killing blacks. Less than four percent of the executions carried out since $1977$ in the USA were for crimes involving Hispanic victims. Hispanics represent about $12$ percent of the US population. Between $1993$ and $1999$, the recorded murder rate for Hispanics was more than 40 percent higher than the national homicide rate.”

(Source: Amnesty International. “United States of America: Death by discrimination-the continuing role of race in capital cases.” AMR $51/046/2003$)

a. In the above quote, what conditional probability is $80\%$? That is, find events $A$ and $B$ such that $p\left(A|B\right)=80\%$.

b. In the above quote, what conditional probability is $13\%$? That is, find events $C$ and $D$ such that $p\left(C|D\right)=13\%$.

c. Use the information in Exercise $49$ to compute $p\left(A|B\right)$ for $1981$.

d. Use the information in Exercise $49$ to compute $p\left(C|D\right)$ for $1981$.

e. Have things improved since $1981$? Justify your answer.