#[Binomial random variable][Variable aleatoria binomial]#

#[A Bernoulli trial is an experiment with two possible outcomes, called success and failure. A binomial random variable $X$ counts the number of successes in a sequence of a fixed number $n$ of independent Bernoulli trials with fixed probability of success $p$ and probability of failure $q = 1-p$.][Un ensayo de Bernoulli es un experimento con dos resultados posibles, denominados éxito y fracaso. Una variable aleatoria binomial $X$ cuenta el número de éxitos en una secuencia de un número fijo $n$ de ensayos independientes de Bernoulli con probabilidad fija de éxito $p$ y probabilidad de fracaso $q = 1-p$.]#

#[Examples][Ejemplos]#

• Flip a coin 10 times; $X$ = Number of heads. $n = 10, p = 1/2, q = 1/2$
• Roll a die 100 times; $X$ = number of fives you roll. $n = 100, p = 1/6, q = 5/6$
• Provide a property in Puerto Vallarta with flood insurance for 20 years in a zone where flooding occurs every five years on average; $X$ is the number of years, during the 20-year period, during which the property is flooded. $n = 20, p = 1/5, q = 4/5$
• Test 50 randomly selected circuits as they come off an assembly line in which 1% of the circuits are defective; $X$ = Number of defective circuits. $n = 50, p = .01, q = .99$