Stats Question

[PlasmaBomb]

Really easy stats question I want to check if I have right.

Population size is ~1800, 350 people are chosen at random out of it.

If a group of 6 people have a common characteristic what is the probability that 5 out of them (the six) are chosen.

Thanks for your time.

 

[sjwaste]

350/1800 = .194, so each person has roughly a 20% chance of getting picked to begin with. If its random, the common characteristic doesn't matter. Therefore the odds of 5 specific people being chosen is .194^5 = .000277 or 0.03%?

Or am I off?

 

[DrPizza]

there are 1800 combination 350 ways to choose your 350 people.

There are (6C5)* (1794C345) ways to select a group of 350 such that exactly 5 of your 6 are in the group of 350.


So, (6C5)(1794C345)/(1800C350)
Knowing what those mean and how to expand them would be helpful; I don't know if calculators can handle it without a bit of simple cancelling first.

 

[dealmaster00]

calculators should be able to handle that just fine.

 

[PlasmaBomb]

Originally posted by: DrPizza
there are 1800 combination 350 ways to choose your 350 people.

There are (6C5)* (1794C345) ways to select a group of 350 such that exactly 5 of your 6 are in the group of 350.


So, (6C5)(1794C345)/(1800C350)
Knowing what those mean and how to expand them would be helpful; I don't know if calculators can handle it without a bit of simple cancelling first.

I get ->
(6C5)(1794C345)/(1800C350) = 1.3 x10^-13 (had to use windows cal as I didn't have a graphical calc handy, hehe i didn't think that would work )

So the chances of you choosing 5 correctly are the reciprocal (1 in 7.69 x10^12) right?