# Fender Avril Lavigne Giveaway

I entered the “Fender Avril Lavigne Giveaway.”

It says

“Want to double your chances of winning?

Share this sweepstakes using the share icons below.
When one of your friends enters…
You get an extra entry*!
* Maximum of one extra entry person Double?

Let x, y > 0. Let P(me winning|I do not share) $= \frac{1}{x}$, and let P(me winning|I share) $= \frac{2}{x+y}$ where $x = \left | A \right |$ and $y = \left | B \right |$ where $A$ = {people who would have known about this even if I did not share} and $B$ = {people who know about this specifically because I shared} = {people who know about this} \ A. $\underline{Assumption \ 1}$: The number of people who would have known about this had I not shared is greater than the number of people who know about this specifically because I shared. $\underline{Proposition \ 2}$: The probability of me winning if I share is greater. $\underline{Pf:}$** $y < x$ (by assumption 1) $x+y < 2x$ $\frac{1}{x} < \frac{2}{x+y}$.

My increased probability is $f(x,y) = \frac{2}{x+y} - \frac{1}{x} = \frac{x-y}{(x)(x+y)}$. $\underline{Corollary \ 3:}$My chances of winning is not doubled if I share it. $\underline{Pf:}$

y≠0 => 2P(me winning|I do not share)≠P(me winning|I share) $\underline{Exercise:}$ Explain the meaning of $f(x,y)$ as $y \to x$, if any.

Note: P(me winning) = P(I do not share) P(me winning|I do not share) + P(me winning|I share) P(I share) by Bayes’ Theorem