Question

Question 6


An experiment consists of rolling a single die 12 times and the variablex is the number of times that the outcome is 6. Use binomial distribution to find the probability that the


outcome of 6 occurs exactly 3 times

Answer 1

Answer:

$P(X=3)$

And using the probability mass function we got:

$P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974$

Step-by-step explanation:

Let X the random variable of interest "number of times that 6 appears", on this case we now that:

$X \sim Binom(n=12, p=1/6)$

The probability mass function for the Binomial distribution is given as:

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

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X=3)$

And using the probability mass function we got:

$P(X=3)= (12C3)(\frac{1}{6})^3 (1-\frac{1}{6})^{12-3}=0.1974$