02 Hypergeometric Distributions

Which is the correct formula to find the probability of any instance of a hypergeometric random variable  $x$  ?

•  $\frac{n_k^{\ \ C}x^{\ \cdot\ }\left(n-n_k\right)^C\left(r-x\right)}{_nC_r}$  

•  $\frac{n_k^{\ \ C}x^{\ \cdot\ }\left(n-n_k\right)^C\left(x-r\right)}{_nC_x}$  

•  $\frac{n_k^{\ \ C}x^{\ \cdot\ }\left(n-n_k\right)^C\left(r-n\right)}{_nC_r}$  

•  $\frac{n_k^{\ \ C}r^{\ \cdot\ }\left(n-n_k\right)^C\left(r-x\right)}{_nC_r}$  

What is the correct formula to find the mean of any hypergeometric random variable  $x$  ?

•  $\mu_x=r\cdot\frac{n_k}{n}$  

•  $\mu_x=n\cdot\frac{n_k}{r}$  

•  $\mu_x=r+\frac{n_k}{n}$  

•  $\mu_x=n+\frac{n_k}{x}$  

What is the correct formula to find the variance of any hypergeometric random variable  $x$  ?

•  $\sigma_x^2=\frac{r\cdot n_k\cdot\left(n-r\right)\cdot\left(n-n_k\right)}{n^3-n^2}$  

•  $\sigma_x^2=\frac{x\cdot n_k\cdot\left(n-r\right)\cdot\left(n-n_k\right)}{n^3+n^2}$  

•  $\sigma_x^2=\frac{r\cdot n\cdot\left(n_k-r\right)\cdot\left(n_k-n\right)}{n^3-n^2}$  

•  $\sigma_x^2=\frac{r\cdot n_k\cdot\left(n-r\right)\cdot\left(n-n_k\right)}{r^3-r^2}$  

What conditions must be met in order for a random variable to be considered hypergeometric? Check all that apply.

• The outcomes in the underlying sample space were formed by drawing without replacement from a single selection set.

• The outcomes in the underlying sample space were formed by drawing with replacement from a single selection set.

• "x" is defined as the number of times a specific result occurs.

• "x" is defined as the draw on which a specific result occurs for the first time.

Crab Lake contains 20 red crabs and 5 blue crabs. If you are catching crabs, what is the probability that in a catch of 4 crabs you will have exactly two blue crabs?

• 0.1502

• 0.3830

• 0.1664

• 0.0400

Crab Lake contains 20 red crabs and 5 blue crabs. If you are catching crabs, what is the probability that in a catch of 4 crabs you will have at least two blue crabs?

• 0.1664

• 0.1502

• 0.8336

• 0.8498

As  $\frac{r}{n}\rightarrow0$  , the hypergeometric distribution starts to look more and more like the...

• binomial distribution
  

• "C over C" distribution
  

• geometric distribution
  

• general probability distribution
  

A hand of five cards is drawn from a standard deck. What is the probability that this hand will contain exactly three face cards?

• 0.0660

• 0.0739

• 0.9340

• 0.9261

A hand of five cards is drawn from a standard deck. What is the probability that this hand will contain less than three face cards?

• 0.9261

• 0.0739

• 0.1154

• 0.6555

A hand of five cards is drawn from a standard deck. What is the expected number of face cards in this hand?

• 1.15

• 4.33

• 2.17

• 0.23