If We Sample from a Small Finite Population Without Replacement $\text { A and } ( n - x )$

question 29

Multiple Choice

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 $\text { A and } ( n - x )$ 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 3 numbers from 1 to 12 (without repetition) , and a winning 3-number combination is later randomly selected. What is the probability of getting all 3 winning numbers? Round your answer to four decimal places.

• A) 0.0065
• B) 0.0045
• C) 0.0055
• D) 0.0035

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Definitions:

Dielectric

Something that limits or blocks current flow. Nonconducting dielectric material is used between poles in a capacitor and dielectric grease can be used to protect exposed terminals.

Conductors

Materials that allow the flow of electrical current, commonly used in electrical wiring and electronics for the transmission of electricity.

Voltage Drop

A decrease in electrical potential along the path of a current through a circuit.

Ohm Resistor

An electrical component that opposes the flow of current, defined by its resistance value in ohms.