Better off dead

Probability Level 1

There is a mob of 3000 people, 1 of whom is a zombie while the other 2999 are not.

Every minute, all 3000 people form 1000 groups of three.
If there are any zombies in a group of three, all three end up zombies.

What is the probability that after 5 minutes there will be exactly 100 zombies in the mob?

Please provide up to 5 decimal places as necessary.

The answer is 0.00.

1 solution

Geoff Pilling
Oct 21, 2016

After each minute the number of zombies will necessarily be divisible by 3 since each group will end up being either all zombies or all non-zombies. Since 100 isn't divisible by three, there will never be exactly 100 zombies in the group. Therefore, the probability is $\boxed{0}$

Dude, and if there is a group of 2 zombies and 1 person, or 3 zombies in a group?

Ron Balter - 4 years, 7 months ago

What happens then? Since there are some zombies in the group, every person becomes a zombie. So we have zombies in groups of 3.

Calvin Lin Staff - 4 years, 7 months ago

I changed the phrasing from "at least one zombie" to "any zombies". Do you think that makes it clearer?

Geoff Pilling - 4 years, 7 months ago

awesome question, just write decimals OK near the answer so as not to give a hint that answer is an integer

Ajinkya Shivashankar - 4 years, 7 months ago

Great suggestion @Ajinkya Shivashankar ... Will do! @Calvin Lin is there a way to do this if the answer is an integer?

Geoff Pilling - 4 years, 7 months ago

I've converted this into a decimal answer.

In future, if you want "0" to be stored as a decimal answer, just enter it as "0.0".

Calvin Lin Staff - 4 years, 7 months ago

@Calvin Lin – OK, sounds good!

Geoff Pilling - 4 years, 7 months ago

not perfect answer

Muralidhar Rao - 9 months, 2 weeks ago

Better off dead

The answer is 0.00.

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