Probability that 12 have purchased yellow gold diamond rings

[eatinbyzombies3]

Let’s also say that 65% of all diamond rings sold in WV are yellow gold. In a random sample of 20 folks, what is the probability that 12 have purchased yellow gold diamond rings?


thank you and I promise this is the last question today.

 

[Jameson]

re: probability that 12 have purchased yellow gold diamond rings

Hopefully someone else will confirm this approach, but it seems like you can interpret this to be a binomial random variable. If not then my apologies in advance. Let's say that $P[\text{gold}]=0.65$.

The general formula for a binomial random variable is:

\(\displaystyle P[X=k]=\binom{n}{k}p^{k}(1-p)^{n-k}\)

where $p$ is the success probability, $n$ is the number of trials and $k$ is the number of successes. Can you fill in the information?