Quick Maths Q (1 Viewer)

[chin0o]

lets say I have a population of 120, and I randomly select 15 at a time, 72 times.
Whenever I select my batch of 15, I put them back in the pool, so they might be selected again. How many from the total pool should I expect never got picked?

Thanks for the help.

 

[carny]

I dont see how you can get a definitive answer.. pretty shit question.. its could be anything from 105 (the same 15 get picked 72 times) to 0 (everyone gets picked at least once) I would think itd be much closer to 0 than 105 because probability of picking the same 15 people 72 times in a row is pretty ridiculous.. but nothing is impossible.. so yeh theres no answer.. probally wrong but i'm thinking 0.

 

[davidbarnes]

Is it even possible to solve it using that little info?

 

[chin0o]

Okay, thanks for the help guys.

I know it was worded pretty badly, so thanks for the big effort webby234, lol.

Cheers!

 

[tristambrown]

population of 120,
select 15 at a time (prob of selction = 15/120 not selection 105/120)
72 times.
I put them back in the pool WITH REPLACEMENT

How many from the total pool should I expect never got picked?


prob of not being selected each time is (105/120) so out of the whole lot of choices it is it's probability times itseld for the number of selections
ie

(105/120))^72 = 0.00006676976


If there was no replacement however you would have to use binomial probability

nCk (a)^n-k (b)^k

where N is number of options
(c is the actual nck fuinction on yur calc)
k is number of times chosen
a is prob of unwanted event
b is prob of wanted event


the prob of not being selected with NO replacement is:
[ 120C72 ((15/120)^(120-72)) ((105/120)^(72))]
= 2.634811924 * 10^-14

 

[tristambrown]

Yea but binomial prob makes so many tree diagrams irrelevant saving so much time in exams - it's a fairly simple concept that actually pays off (coz there is always an involved probability question in the 2u papers)