The Geometric Distribution (Edexcel A-Level Further Mathematics): Flashcards

Game: win/lose, play up to & including first win

$X \sim \text{Geo}(p)$, $p$=P(win), $X$=trials to 1st win

Trials are independent

Fixed probability of success

$P(X=n)=(1-p)^{n-1}p$

$n-1$ losses, then 1 win

$(1-p)^n$

$P(X > n-1)$

$1 - P(X > n)$ or $1-(1-p)^n$

$(1-p)^{a-1}-(1-p)^{b-1}$