in the following experiment, determine whether or not the probabilities are binomial probabilities. if they…

in the following experiment, determine whether or not the probabilities are binomial probabilities. if they are, identify the values for n, p, and q. a pair of dice are rolled 100 times. what is the probability of getting doubles x times? a. binomial probability; n = 12, p = 1/6, q = 5/6 b. binomial probability; n = 12, p = 1/12, q = 11/12 c. binomial probability; n = 100, p = 1/6, q = 5/6 d. not a binomial probability

in the following experiment, determine whether or not the probabilities are binomial probabilities. if they are, identify the values for n, p, and q. a pair of dice are rolled 100 times. what is the probability of getting doubles x times? a. binomial probability; n = 12, p = 1/6, q = 5/6 b. binomial probability; n = 12, p = 1/12, q = 11/12 c. binomial probability; n = 100, p = 1/6, q = 5/6 d. not a binomial probability

Answer

Explanation:

Step1: Comprender los requisitos binomiales

Un experimento binomial tiene un número fijo de ensayos $n$, cada ensayo es independiente, solo hay dos resultados posibles (éxito o fracaso), y la probabilidad de éxito $p$ es constante en cada ensayo.

Step2: Identificar $n$, $p$ y $q$

Se tiran dos dados 100 veces, entonces $n = 100$. El éxito es obtener dobles. Cuando se tiran dos dados, hay 36 posibles resultados y 6 casos de dobles ($(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)$). Así, $p=\frac{6}{36}=\frac{1}{6}$. Y $q = 1 - p=1-\frac{1}{6}=\frac{5}{6}$.

Answer:

C. Binomial probability; $n = 100,p=\frac{1}{6},q=\frac{5}{6}$