# Jury selection, racial bias, and probability?

#### stud40111

##### New member
Me again. Sorry to ask two questions on my first night here, but I've tried for about an hour to figure out this very simple problem and can't understand this one either.

If jurors are selected randomly from an adult population, find the probability that all 12 jurors are white when the population is

a) 90% white

b) 50% white

WHAT IS CONFUSING ME:

How in the world can a person figure this out when one doesn't know what the city's population is?

THere's an example of a very similar problem in my book that says that if 50% of a town's population were female, and 50% male, the probability that the jury would be all male is only .00024 and that they somehow determined this from the fact that there are only 4096 possible ways that a jury of 12 can be composed. I have no idea what they are talking about.

Can anyone should some light? If so, PLEASE DO.

#### wjm11

##### Senior Member
If jurors are selected randomly from an adult population, find the probability that all 12 jurors are white when the population is

a) 90% white

b) 50% white

THere's an example of a very similar problem in my book that says that if 50% of a town's population were female, and 50% male, the probability that the jury would be all male is only .00024 and that they somehow determined this from the fact that there are only 4096 possible ways that a jury of 12 can be composed. I have no idea what they are talking about.
There are 12 spots on the jury. For each spot there is a .5 chance a man will be chosen. Multiply all the possibilities together:

(.5)(.5)(.5)(.5)(.5)(.5)(.5)(.5)(.5)(.5)(.5)(.5) = .5^12 = .000244

If you are working with a population that is 90% white, then there is a .9 chance a white person will be chosen for each spot. You don’t need to know the population of the city.