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:

Corporate Insurance

A type of insurance coverage designed to protect corporations from financial losses due to events such as property damage, liability claims, and employee-related risks.

Liability Insurance

Insurance protection that offers defense against claims related to harm or damage inflicted on other individuals or their property.

Property Damage

Harm or destruction that affects the value or usability of someone's property.

Dash Delivery

A rapid delivery service that aims to transport items to customers in a very short time frame, often leveraging technology for efficiency.