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Using Probability in Court Trials

1. In 1972, Rodrigo Partida, a Mexican-American, was convicted of burglary with intent to commit rape. His conviction took place in Hidalgo County, which is in Texas on the border with Mexico. In Hidalgo County, 79.1% of the residents eligible for jury selection are Mexican-American. Partida's conviction was later overturned because an appellate judge decided he was not truly tried in front of a jury of his peers. The jury that tried Rodrigo Partida consisted of 7 Mexican-Americans out of 12 jurors. Answer the following questions to decide if you agree or disagree with the appellate judge's ruling.

a. What is the probability that a single randomly selected juror from Hidalgo County is Mexican-American? Explain briefly.

b. What is the probability a single randomly selected juror is not Mexican-American? Explain briefly.

c. If x represents the number of jurors out of twelve that are Mexican-American, what would be the values of n and p? Explain briefly.

d. What is the probability that 7 or less of the 12 jurors would be Mexican-American? Please be sure to show all of your work.

e. Based on your answer in part c, do you agree with the appellate judge's ruling? Why or why not? Please be specific and completely justify your answer.

Solution Preview

a. What is the probability that a single randomly selected juror from Hidalgo County is Mexican-American? Explain briefly.

Since we are told that 79.1% of the residents of Hidalgo County that are eligible for jury selection are Mexican-American, it makes sense that if we randomly selected just one juror from all of the residents of Hidalgo County who are eligible for jury selection, the probability that the person selected would be Mexican-American is 79.1%, or 0.791 (in decimal form).

b. What is the probability a single randomly selected juror is not Mexican-American? Explain briefly.

If 79.1% of the residents of Hidalgo County that are eligible for jury selection are Mexican-American then the rest of them must NOT be Mexican-American. Since 100% - 79.1% = 20.9%, 20.9% of the residents of Hidalgo County who are eligible for jury selection are NOT Mexican-American. So now, by reasoning similar to that used to answer question 1, it follows that if we randomly selected just one juror from all of the residents of Hidalgo County who are eligible for jury selection, the probability that the person selected would NOT be ...

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The solution discuses using probability in court trials.

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