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:

Straight-Bond Value

The value of a bond calculated without considering any embedded options, based purely on its coupon payments and maturity value.

Conversion Value

The monetary value of a convertible security if it were converted into a different form, usually shares of the company's common stock.

Call Options

Financial derivatives that give the holder the right, but not the obligation, to buy an underlying asset at a predetermined price within a specific timeframe.

Stock Options

Contracts that give the investor the right, but not the obligation, to buy or sell a stock at a specified price before a certain date.