zombie probability problem

hamsterofdeath2

New member
Joined
Apr 30, 2018
Messages
9
hi everyone,

i am stuck at the following problem:
we're living in a postapocalyptic world. we know that 2% of all people are going to turn into zombies.
in our case, there are 100 people to be tested. lazy as we are we don't test one by one. instead take a blood sample of each person, mix it, and perform a test. the test tells us that there is at least one zombie among the people, so we didn't get away with just one test ;(

now the question i've been trying to answer for days:
if i take a mixed blood sample of N people, how do i calculate the probability of a positive result?
had i not done the first initial test, it would just be 0.98^N to get the probability that my N people are fine. what's the function/formula for my new case?
 
hi everyone,

i am stuck at the following problem:
we're living in a postapocalyptic world. we know that 2% of all people are going to turn into zombies.
in our case, there are 100 people to be tested. lazy as we are we don't test one by one. instead take a blood sample of each person, mix it, and perform a test. the test tells us that there is at least one zombie among the people, so we didn't get away with just one test ;(

now the question i've been trying to answer for days:
if i take a mixed blood sample of N people, how do i calculate the probability of a positive result?
had i not done the first initial test, it would just be 0.98^N to get the probability that my N people are fine. what's the function/formula for my new case?

Sometimes, you just have to make up a different question - one that is lots easier - and answer that instead.

What is the probability that of your N samples there will be NONE with Zombie disease?

Pr(just one is clear) = 0.98
Pr(two are clean) = 0.98^2
etc.

Pr(at least one) = 1 - Pr(none)
 
"What is the probability that of your N samples there will be NONE with Zombie disease?"

this is exactly the question i do not find the answer for. your proposal does not work. let me show you:
Pr(all are clean) = 0.98^N

so if my group i am about to test is 100 people (of 100), the chance of all being clean would be 0.98^100 according to your solution. but since i already made a pre test, i know there is at least one zombie, so the correct formula must give "0" in this case.
 
"What is the probability that of your N samples there will be NONE with Zombie disease?"

this is exactly the question i do not find the answer for. your proposal does not work. let me show you:
Pr(all are clean) = 0.98^N

so if my group i am about to test is 100 people (of 100), the chance of all being clean would be 0.98^100 according to your solution. but since i already made a pre test, i know there is at least one zombie, so the correct formula must give "0" in this case.

You are confusing your samples. Your N potential zombies are not the same as those in the pre-test.

If you do a pre-test of 100, the probability that there I no zombie is as stated IN THE PRE-TEST, 1 - 0.98^100

If you then draw a DIFFERENT SAMPLE, it is also as stated, 1 - 0.98^N. These are independent samples. Or, are you adding N-100 additional potential zombies to create a dependent sample of N total that incudes the original 100?

If your result is to give zero (0), you must be doing a census, not a sample. Samples don't work that way.
 
i am not confusing anything.

"Your N potential zombies are not the same as those in the pre-test."

they are.
there are 100 people in total.
i test them all at once. result positive -> at least one of them is a zombie

now i take N people of those i just tested (for example 10) and do the same test with those 10. the probability of them being all healthy must be lower than 0.98^10 because i already have the knowledge that there is at least one zombie among the 100 people.
 
Top