In 1981, a study on race and the death penalty was released. The data in the table below are from that study.
Death penalty imposed? | Victim's race | Defendant's race | Frequency
----------------------|--------------|------------------|----------
Yes | White | White | 17
Yes | White | Black | 14
Yes | Black | White | 0
Yes | Black | Black | 6
No | White | White | 134
No | White | Black | 158
No | Black | White | 8
No | Black | Black | 98
The information above is rather dated. Use the following information to determine whether things have improved since then.
In April 2003, Amnesty International issued a study on race and the 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 are the victims 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."
(a) In the above quote, what conditional probability is 80%? That is, find events A and B such that p(A|B) = 80%.
(b) In the above quote, what conditional probability is 13%? That is, find events C and D such that p(C|D) = 13%.
(c) Use the information from the study in 1981 to compute p(A|B) for 1981. (Round your answer to one decimal place.)
(d) Use the information from the study in 1981 to compute p(C|D) for 1981. (Round your answer to one decimal place.)
(e) Have things improved since 1981? Justify your answer.