Probabilty Help

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Probabilty Help

by mwrice93 » Sat Jul 01, 2017 12:45 pm
Can anyone help me with this probability question?
Jury selection is a highly important process. The prosecution and defense are looking for the best possible jurors to consider their arguments. For example, in a domestic violence or sexual assault case, the prosecution would likely prefer a jury sympathetic to the victim. The defense, on the other hand may not. The challenge becomes not only agreeing on a jury panel but finding jurors that fit their criteria.
Considering a hypothetical abuse case in a city of size 400,000 with approximately equal numbers of men and women. Furthermore, assume that 60% of its residents know a victim of abuse. About 14% of men have been victims and 30% of women. (The group "No More" recently released these results.)

1.In a jury pool of 300 people, how many different groups of 40 potential jurors are possible?
2.How many 12-person juries are possible among a given group of 40?
3.What is the probability that a person chosen knows a victim of domestic or sexual abuse?
4.What is the probability that a person chosen is female or a victim of abuse?

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by [email protected] » Sat Jul 01, 2017 3:28 pm
Hi mwrice93,

What is the source of this prompt? And are you studying for the GMAT or for some other Exam/Class?

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by Matt@VeritasPrep » Wed Jul 05, 2017 1:13 am
mwrice93 wrote: 1.In a jury pool of 300 people, how many different groups of 40 potential jurors are possible?
Assuming you have no restrictions on the jurors, this is 300 choose 40, or 300! / (40! * 260!). I doubt your prof would want you to actually work out that number. :)

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by Matt@VeritasPrep » Wed Jul 05, 2017 1:13 am
mwrice93 wrote: 2.How many 12-person juries are possible among a given group of 40?
Much like the first problem, this is 40 choose 12, or 40! / (12! * 28!). Again, you should be able to leave the answer in that form.

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by Matt@VeritasPrep » Wed Jul 05, 2017 1:15 am
mwrice93 wrote: 3.What is the probability that a person chosen knows a victim of domestic or sexual abuse?
This is unanswerable because we don't know how the person is chosen. Assuming (s)he is chosen at random, it's about 60%, since we're given 60% of the sample knows a victim of domestic or sexual abuse. We'd want to know whether knowing yourself counts (some of the abuse survivors may not know any other victims, so the number could be higher than 60%).

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by Matt@VeritasPrep » Wed Jul 05, 2017 1:17 am
mwrice wrote:4.What is the probability that a person chosen is female or a victim of abuse?
Half the city are female, so that's 50%. That includes all the female victims, leaving us with only the males to add. Of the male 50%, 14% are victims, so 14% * 50%, or 7%.

Summing those, we get 57%.