If We Sample from a Small Finite Population Without Replacement $$P ( x ) = \frac { A ! } { ( A - x ) ! x ! } \cdot \frac { B ! } { ( B - n + x ) ! ( n - x ) ! } \div \frac { ( A + B ) ! } { ( A + B - n ) ! n ! }$$

question 121

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 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 4 numbers from 1 to 14 (without repetition) , and a winning 4-number combination is later randomly selected. What is the probability of getting all 4 winning numbers?

• A)0
• B)0.002
• C)0.001
• D)0.003

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Definitions:

Ethical Problem

An Ethical Problem involves a situation where a decision must be made that could conflict with moral principles or ethical standards.

Limited Supply

A situation in which the availability of a product or resource is not sufficient to meet demand, leading to potential scarcity.

Distribution

The process of making a product or service available for use or consumption by a consumer or business user.

Ethical Principles Screen

A framework used to evaluate moral concerns, ensuring actions align with core ethical values such as justice, autonomy, and beneficence.