# Fender Avril Lavigne Giveaway

I entered the “Fender Avril Lavigne Giveaway.”

It says

“Want to double your chances of winning?

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