The Binomial Distribution Applies Only to Cases Involving Two Types $\mathrm { A } , \mathrm { B }$

question 35

Multiple Choice

The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes denoted by $\mathrm { A } , \mathrm { B }$ , and $\mathrm { C }$ . Let $\mathrm { P } ( \mathrm { A } ) = \mathrm { p } _ { 1 } , \mathrm { P } ( \mathrm { B } ) = \mathrm { p } _ { 2 } , \mathrm { P } ( \mathrm { C } ) = \mathrm { p } _ { 3 }$ . In $n$ independent trials, the probability of $\mathrm { x } _ { 1 }$ outcomes of type $\mathrm { A } , \mathrm { x } _ { 2 }$ outcomes of type $\mathrm { B }$ , and $\mathrm { x } _ { 3 }$ outcomes of type $\mathrm { C }$ is given by
$$\frac { n ! } { \left( x _ { 1 } \right) ! \left( x _ { 2 } \right) ! \left( x _ { 3 } \right) ! } \cdot p _ { 1 } { } ^ { x _ { 1 } } \cdot p _ { 2 } { } ^ { x _ { 2 } } \cdot p _ { 3 } { } ^ { x _ { 3 } }$$ A genetics experiment involves four mutually exclusive genotypes identified as A, B, C, and D, and they are all equally likely. If 13 offspring are tested, find the probability of getting exactly 3 A's,2 B's,3 C's, and 5 D's by expanding the above expression so that it applies to four types of outcomes instead of only three. Round your answer to five decimal places.

• A) 1.28875
• B) 0.01074
• C) 0.00268
• D) 0.04296

---

Definitions:

Economic

Economic refers to anything related to the production, distribution, and consumption of goods and services, and how they affect the wealth of a society or an individual.

Traditional Nuclear Family

A family structure typically consisting of two parents (one male, one female) and their biological children living together.

Latchkey Family

A family arrangement where children are left to care for themselves for part of the day, often because parents are at work or away.

Employed Full-Time

Refers to having a job or position that requires the standard number of hours per week defined by an employer as full-time work.