The Binomial Distribution (Edexcel A-Level Mathematics): Flashcards

$X$ is the number of wins in $n$ trials with success $p$.

Win or lose in a fixed number of trials.

Probability of success (winning) in each trial.

Number of trials performed in the game.

Mean is $np$, where $n$ is trials and $p$ is probability.

Variance is $np(1-p)$.

$P(X = x) = C(n, x) p^x (1-p)^{n-x}$.

$C(n, x)$ is the binomial coefficient, $n!/(x!(n-x)!)$.

$X \sim B(8, 1/3)$.

Probability of getting 0 or 1 successes.