TITLE: What's the probability of me being obliterated if Thanos snaps his fingers twice?
QUESTION [6 upvotes]: Thanos snaps his fingers and half the Earth's population disappear. He snaps again and half of the remaining half disappear. Now, what is the probability of any given person (for example, myself) disappearing after 2 snaps?
My simplistic reasoning was that, since after 2 snaps 75% of the population are gone, it means that any one person (e.g. me) has a 75% chance of having been eliminated as well.
My friend's asking for a formula, i.e. mathematical proof of this calculation and the best I can come up with is:

event (snap): 50% chance of being obliterated
event (snap): 50% chance of having survived the first snap and another 50% chance of perishing so 50% x 50% = 25%
Sum of two events = 50% + 25% = 75%

Could someone please verify if my logic is sound and what's the correct math behind it.
Thanks so much!

REPLY [5 votes]: Let $E_1$ denote the event that the person was not eliminated by the first snap.
Let $E_2$ denote the event event that the person was not eliminated by the second snap.
Then, a person survives if and only if events $E_1$ and $E_2$ both occur.
$p(E_1,E_2) = p(E_1) \times p(E_2|E_1).$ 
You are given that :

$p(E_1) = (1/2).$
$p(E_2|E_1) = (1/2).$

Note that this approach bypasses any need to consider whether any events are independent of each other.

The confusing part of this problem is that you are actually given $p(E_2|E_1)$, rather than being given $p(E_2)$.