Provide an Appropriate Response $P ( x ) = \frac { A ! } { ( A - x ) ! x ! } \cdot \frac { B ! } { ( B - n + x ) ! ( n - x ) ! } \div \frac { ( A + B ) ! } { ( A + B - n ) ! n ! }$

Multiple Choice

Provide an appropriate response.
-If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to
One of two types, we can use hypergeometric distribution. If a population has A objects of one type, while the
Remaining B objects are of the other type, and if n objects are sampled without replacement, then the probability
Of getting x objects of type A and (n - x) objects of type B is $P ( x ) = \frac { A ! } { ( A - x ) ! x ! } \cdot \frac { B ! } { ( B - n + x ) ! ( n - x ) ! } \div \frac { ( A + B ) ! } { ( A + B - n ) ! n ! }$ In a relatively easy lottery, a bettor selects 5 numbers from 1 to 13 (without repetition) , and a winning 5-number
Combination is later randomly selected. What is the probability of getting all 5 winning numbers? Round your
Answer to four decimal places.

A) 0.0028
B) -0.0002
C) 0.0008
D) 0.0018