6 people. (1 person lives 100%, 5 die 100%) or (1 dies 100%, 5 live 20%)

This, like you say, is a choice between guaranteed 1 person living, or leaving it up to chance where

*on average* 1 person lives. (5 people taking a 1/5 chance)

101 people. (1 person lives 100%, 100 die 100%) or (1 dies 100%, 100 live 1%)

This again proves that on average, 1 person will live no matter which decision you choose. (even if there were 100 treatments)

So the question then is, do you decide to risk that 1 person survival rate, for more.

Telling 100 people they have a 1% chance to live...

You can go to a casino and figure out that thousands of people can play a game with 1% chance to win before someone wins (without any rigged game or machine).

Chance, randomness, is supposed to exactly define the unknown and/or unpredictable elements of something.

This means you're just as likely to have 0 survivors as you could have 2 survivors, let alone 3.

Check this out:

A script to test the chances for 100 people. On the last few tests it happened to catch up, and the last test 4 people survived, just to reach the expected result out of the arbitrary number of tests chosen to take. (100 tests)

Try it for yourself and see:

jsfiddle.net/ecb1kyn2/(keep in mind that this test is for the remaining 100 people out of 101; 1 already died because they can't get the 100 treatments you are risking with the 100 people for 1% chance to live)

But after writing this script, I did notice something:

If you're just as likely to get 0 as you are 2, then in the scope of (0, 1, 2), there is a 2/3 chance to have a winning result.

So I ran the test a few more times, in groups of 3 to see the results:

1) 5 people / 3 tests = 166.67%

2) 3 people / 3 tests = 100%

3) 2 people / 3 tests = 66.67%

4) 8 people / 3 tests = 266.67%

5) 4 people / 3 tests = 133.33%

So now I'm fairly convinced that either my script, or randomness, isn't accurate, or that I should risk it every time. :s