Suppose you have a full deck of cards and you randomly choose 6 cards without replacement. What is the probability that you will choose exactly 2 kings?
In this example, drawing a king from the deck of cards can be considered a success, meaning that since there are 4 kings in the deck of cards, there are 4 successful states.
Let population size, N, be 52, number of successful states (the number of kings in the deck of cards), K, be 4, number of draws, n, be 6, and number of successes, k, be 2.
$f\left(Xequals;4\right)equals;P\left(Xequals;k\right)equals;\frac{\left(\genfrac{}{}{0ex}{}{4}{2}\right)\left(\genfrac{}{}{0ex}{}{52-4}{6-2}\right)}{\left(\genfrac{}{}{0ex}{}{52}{6}\right)}$ = 0.057346.
The probability of randomly choosing 6 cards without replacement and obtaining exactly 2 kings is 0.057346 or 5.7%.